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Weekend Watch List: Kevin Smith! Pumpkin DJ's! Yanks and Phils Still Fighting!
Welcome to Watch List, where we identify five things on TV to watch while you stay at home and start your own political party. Squirrels deserve a voice in this country too, you know. Why are we so lacking in acorn subsidies? Have we no compassion? LET'S GO!
KEVIN SMITH: TOO FAT FOR FORTY – 9:30PM Saturday (Epix) The writer/director takes a timeout from making incredibly average movies to do what he does best: stand on a stage and talk. Tonight he plays to a packed house in Jersey, to tell stories about Hollywood and presumably address his little dustup with Southwest Airlines a while back. At what point can we stop referring to Smith as a director and start referring to him as a standup comic? Because really, that's his true calling, isn't it? I think he makes crummy movies specifically just so that he has a good story to tell later on. Shouldn't he stop making movies and just tour the country with Patton Oswalt? I don't need him making "Zack and Miri 2" anymore. ANTICIPATION: DIRTY!
MY SUPER PSYCHO SWEET SIXTEEN 2 – 10:00PM Tonight (MTV) Ever watch one of MTV's old "My Super Sweet 16" shows and want the spoiled brat featured to die? MTV feels your pain, which is why they're trotting out this second made-for-TV movie in which a birthday party ends up with numerous slashings and other gory delights. Oh, you wanted a pink Porsche, missy? YOU WILL HAVE A BLADE TO THE GUT AND LIKE IT. ANTICIPATION: SLASHY!
YANKEES/RANGERS, GAME 5 – 8:07PM Tonight (TBS) Down three games to two, the Yankees need to sweep Texas in Texas to claim their second consecutive AL pennant. If the Rangers can stop them and move on to the World Series, expect many a gun to be fired in the air. YEEEEEEHAWWWWW WE DONE DID IT! ANTICIPATION: HIGH!
SHERLOCK – 9:00PM Sunday (PBS) PBS trots out this extremely contemporary version of Arthur Conan Doyle's legendary character. This Sherlock Holmes texts and blogs and is, like, OMG SO FINE. He's played by Benedict Cumberbatch, which is the Britishest name I have ever heard and ever will hear. ANTICIPATION: SLEUTHY!
GROWING THE BIG ONE – 9:00PM Saturday (Hallmark Channel) Just in time for Halloween comes this weepie starring Shannen Doherty about a DJ (!) who inherits a pumpkin farm (!!) and then finds true love (!!!). Throw in that suggestive title and this could very well be the best worst thing you watch all week. ANTICIPATION: SHANNEN DOHERTY IS A DJ WHO OWNS A PUMPKIN FARM?


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Monday, October 2nd, 2017, 1:08pm
AMHERST, N.Y. – For the second consecutive year, Daemen College has been ranked nationally in the prestigious Wall Street Journal/Times Higher Education College Rankings, which focus on student success and learning. The second annual list includes 1,054 institutions from across the U.S.
Rankings are based on four key performance areas, including resources (30 percent), engagement (30 percent), outcomes (40 percent), and environment (10 percent).
Based on these four main pillars, Daemen was strongest in the area of engagement, making it the second time the college has ranked high for effectively engaging with students. Specific measures used to assess this are interaction with teachers and students, students feeling engaged with the college, whether students would recommend the institution to a friend, and the number of accredited programs.
Local Educator Hopes to Share His Love for the Great Outdoors with a New, Younger Audience
Wednesday, September 27th, 2017, 9:06am
Dave Bauer made a career out of teaching environmental science to teenagers, and now that he's retired, he wants to cut back a little bit. No, not on teaching students about his love for the environment and the great outdoors. That will never change.
What he would like to do is cut back on the age of the students a wee bit, and bring his message to the kindergarten through grade three population … and their parents, teachers, librarians, principals and school administrators.
'Plant Lady' Sally Cunningham to Host Native Plant Gardening Talk in Niagara Falls
The Western New York Land Conservancy will host a special talk at the Niagara Falls Public Library with featured speaker Sally Cunningham at 7 p.m. Wednesday, Oct. 4. Sally is the author of the nationally popular gardening book "Great Garden Companions" and is well known in Western New York from her regular segments on Channel 4 News and articles in The Buffalo News.
Sally will describe the critical importance of native plants and she will share ways that all Western New Yorkers can use natives in their own yards and gardens, just as the Land Conservancy is doing in the Niagara Gorge.
Buffalo Jazztet's Tribute to Harold Arlen Coming to Kenan Center's Taylor Theater
Monday, September 25th, 2017, 9:30am
The Kenan Center, in collaboration with The Carriage House Players, will present The Buffalo Jazztet in "A Tribute to Harold Arlen" at the Taylor Theater on Saturday, November 4, 2017. This is the third concert in the Kenan Center's 50th Anniversary Jazz Series featuring some top names in jazz – both locally and nationally. The show begins at 7:30 PM in the Taylor Theater, a 153-seat converted carriage house on the Center's campus, providing an intimate, club-like atmosphere. The concert will feature two full sets of music. Refreshments will be available.
Explore Buffalo Announces Special Architectural and Adventure Events
Explore Buffalo is excited to offer another year of the Buffalo Architecture Course and Adventures in Buffalo History Fall Speaker Series!
FALL 2017 ARCHITECTURE COURSE: BUFFALO INTERIORS 101
7 to 8:30 p.m. Tuesday, Oct. 3, 10, 17, 24
Meet: Explore Buffalo's headquarters in First Presbyterian Church of Buffalo (across from Kleinhans Music Hall). Parking is available in the church lot, which can be accessed from Pennsylvania Street, or on any surrounding side streets.
Cost: General $40, Student $35, Explorer Pass $35
Explore Buffalo's Tour are Still Going Strong Through October
Thursday, September 21st, 2017, 2:21pm
Even with the calendar nearly ready to turn to October, there's no slowdown in the amount of quality tours being offered by Explore Buffalo!
TURN OF THE CENTURY TREASURES
9:30 a.m. Oct. 6, 13, 20, 27
Meet: Western New York Book Arts Center, 468 Washington St., Buffalo, corner of Washington and Mohawk streets. Two-hour parking is available on surrounding streets, and the Mohawk Parking Ramp is on the opposite corner. The Lafayette Square Station of the Metro Rail is around the corner on Main Street.
Cost: General $15, Student $5, Explorer Pass Free
WNY Children's Book Expo Returns in November to Encourage Kids to Explore
Thursday, September 21st, 2017, 8:57am
The popular and growing WNY Children's Book Expo (WNYCBE), the area's premier literary event for children, returns in November and will culminate with a special event from 10 a.m. to 3 p.m. Saturday, Nov. 11, in the Buffalo Niagara Convention Center.
The six-day event kicks off with KidsLit Week from Nov. 6-10, during which nearly 40 internationally acclaimed authors will visit area schools, libraries, museums and cultural venues to inspire a love of books in students from pre-k through middle school. Expo Saturday, on Nov. 11, is a day-long showcase of new and beloved books written for kids. Here, local, national and international authors will interact directly with children (and parents, teachers and school officials) through readings, book-signings, presentations and demonstrations.
ST HAGOP CHURCH ARMENIAN FESTIVAL
ST. HAGOP ARMENIAN CHURCH FESTIVAL

redpajama_set_name: RedPajamaCommonCrawl


text:
Etihad Airways boosts capacity between Abu Dhabi and Melbourne
Etihad Airways, the national airline of the United Arab Emirates, will add more seats between Abu Dhabi and Melbourne by introducing a Boeing 777-300ER to the route.
The larger aircraft, to start operating from December 1, will offer 328 seats in a three-class configuration - 36 more than the Airbus A340-600 which is currently flying the Abu Dhabi-Melbourne sector.
Etihad Airways' President and Chief Executive Officer, James Hogan, said the introduction of the larger aircraft reflected the importance to Etihad Airways of the Australian market and Melbourne in particular.
"Etihad Airways' Melbourne–Abu Dhabi flights are some of the strongest performers in our network – this year load factors between the two cities have averaged more than 80 per cent.
"Switching to the Boeing 777 gives us 12 per cent more seats overall and 25 per cent more in business class. This will enable us to increase our share of the corporate and leisure travel market between Australia and Abu Dhabi and beyond to our worldwide network."
Mr Hogan said the introduction of a larger aircraft also presented a growth opportunity for the airline's highly successful cargo division, Etihad Cargo.
"The Boeing 777 offers a bellyhold cargo capacity of around 14-16 tonnes which allows us to capitalise on Australia's strong trading relationship with the United Arab Emirates.
"The United Arab Emirates is Australia's largest trading partner in the Middle East and, last year, two-way merchandise trade between Australia and the UAE was worth around $5.13 billion."
The three-class Boeing 777-300ER has eight seats in Diamond First Class, 40 in Pearl Business Class, and 280 in Coral Economy Class.
Etihad Airways commenced flights between Abu Dhabi and Melbourne in 2009.


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\section{Introduction}
The presentation of a novel approach for view synthesis called Neural Radiance Fields (NeRF) \cite{mildenhall2020nerf} caused an explosion of interest in the field of computer vision. Even though the original paper was presented recently, a large number of follow-up studies have already been published \cite{xie2022neural}. However, NeRF-based methods for clinical use remain largely unexplored. At the same time, there is increasing interest in virtual presence in operating rooms (ORs) during real or simulated surgeries. For example, the National Autonomous University of Mexico used virtual reality to simulate an OR, including distractions and interruptions, to train paediatric surgical residents during the COVID-19 pandemic \cite{perez2020immersive}. Apart from surgical training with virtual reality \cite{seymour2008vr}, physician assistant students can greatly benefit from training in a virtual environment \cite{francis2020operating}.

NeRF is a powerful technology for the reconstruction of a 3D scene from a set of images that capture the scene from various camera positions. Likewise, this technology could be used to build 3D representations of clinical environments such as the OR. NeRF requires only a set of calibrated cameras that capture the scene of interest and does not depend on any physical marker or complex sensory system. When applied to overhead cameras in the OR, NeRF could build 3D reconstructions of the surgical environment, providing the ability to render videos that virtually record surgical scenes. These videos could be used for virtual presence, helping students or clinicians to experience a surgery without the need to be actually present. The advantage over the existing systems for virtual presence in the OR, such as the ones mentioned above, is that NeRF can provide real instead of simulated surgeries.

In this paper, we show how NeRF can be used for view synthesis in the OR.  We show that depth-supervision \cite{deng2022depth} helps to increase the render quality and reduces the need for many camera positions. This is particularly relevant for clinical environments, where it is generally impossible to capture the scene with tens to hundreds of cameras.  In fact, we find that a depth-supervised NeRF with only three or five synchronised camera views captures the surgical field, and is able to generate images of the surgical intervention from a range of camera angles. In contrast to existing depth-supervision in NeRF, we directly optimise our model using  measured RGB-D sensor data instead of estimated depth from a Structure from Motion (SfM) algorithm.

\section{Related work}

\subsection{Neural Radiance Fields}
NeRF is a method for volume rendering, based upon the \textit{implicit representation} of a 3D scene in the weights of a neural network $F_\Theta$ \cite{mildenhall2020nerf}. This network is generally a standard multi-layer perceptron (MLP) that takes a 5D vector $(x, y, z, \theta, \phi)$ as input and that outputs a 4D vector $(RGB, \sigma)$. An input vector consists of a 3D location $(x, y, z)$ in the captured scene and an orientation $(\theta, \phi)$ from which this location is viewed. $F_\Theta$ returns for each vector a colour $RGB$ and a volume density $\sigma$. With this simple setup, NeRF can reconstruct images by casting a viewing ray from each pixel, sampling points along that ray, asking the MLP to find the colours and densities for these points and to sum over these results. In this way, it is possible to use a discrete set of sampled points in the 3D scene, while representing the 3D scene in continuous form. Reconstructed images are compared with ground truth images that are taken from the same camera positions. Importantly, the rendering function that sums over the found colours and densities is differentiable such that the MLP can be optimised by stochastic gradient descent. The loss function is often a total squared error between the colours of the rendered and the ground truth images.

\subsection{NeRF with Depth Priors}
Although the original NeRF has the ability to synthesise photo-realistic images from unseen camera perspectives, there are some limitations. One is that NeRF does not guarantee to capture 3D geometry accurately, which appears to be problematic for poorly textured areas that often occur in indoor scenes \cite{wei2021nerfingmvs}. Additionally, points are randomly sampled along a viewing ray, even though most of these points will describe empty space. It is likely that these problems will play a role when NeRF is applied to scenes in the OR, as these involve a large indoor environment.

Several solutions are proposed that enforce NeRF to find a more accurate geometry by regularisation with depth priors. Nerfing MVS \cite{wei2021nerfingmvs} provides a guided optimisation scheme for NeRF, where points are sampled along a viewing ray only around depth values found earlier. A sparse set of depth values is found by applying the COLMAP SfM algorithm \cite{schonberger2016structure} on the multi-view images. The sparse sets are used to train a depth completion network that provides full sets of depth values. With this optimisation scheme, NeRF is able to provide more accurate depth maps and has a better understanding of the scene's 3D geometry. \cite{neff2021donerf} have shown that computational costs at inference can be reduced significantly when conditioning NeRF on depth information. Their method involves another sampling strategy to include only points located around surfaces. These point locations are predicted by an oracle network.

\cite{roessle2022depthpriorsnerf} present a similar approach to leverage depth priors with depth-guided sampling. Additionally, the authors propose to add a loss term that enforces NeRF to terminate rays close to the most certain depth observations that are provided by a depth completion network. The work by \cite{rematas2022urban} shows how a depth-constrained NeRF is able to reconstruct large urban areas by training the network with an additional loss term as well. The loss enforces NeRF to represent a large amount of volume density around ground truth depth values found with a LiDAR sensor and a small amount in the area along the viewing ray that is closer to the camera. The depth-supervised NeRF \cite{deng2022depth} uses an additional loss function that operates with known depth values from RGB-D data or that are obtained from the COLMAP algorithm. This loss constraints the distribution of ray terminations to be similar to the known depth distribution by minimising the KL divergence between the two. The key insight is that they consider the uncertainty of the known depth values and constrain NeRF proportionally to the uncertainty.

The work above shows that depth priors help to reduce the number of camera poses required for NeRF to synthesise high-quality images. This is particularly relevant for the OR, where it is not possible to put cameras at all locations and the overall number of available cameras is limited.

\subsection{NeRF for Clinical Interventions}
Although NeRF has not been widely adopted in the field of computer-assisted interventions, the technology has been used for 3D reconstruction of soft tissues in robotic surgery videos by \cite{wang2022neural}. Because the laparoscopic view is a single view, their method uses time-dependent modelling of neural radiance and displacement fields, based upon D-NeRF \cite{pumarola2021d}. Using the stereoscopic camera of the surgical robot, the method finds depth maps along the coloured image frames. The depth information is used to constrain NeRF optimisation with an additional loss function.

\section{Methods}

\subsection{Depth-Supervised NeRF}
We use the depth-supervised NeRF (DS-NeRF) by \cite{deng2022depth} for building 3D reconstructions of OR scenes. This method regularises the training with an additional depth loss such that a model can be optimised with relatively few camera positions. The key idea in DS-NeRF is that most viewing rays terminate at the closest surface, which is often opaque. Therefore, most volume density should be found close to the distance of this surface along the viewing ray. DS-NeRF enforces such a distribution of volume density by minimising the KL divergence between the volume density distribution $h_i(t)$ and a normal distribution around the ground truth depth $d_i$ of keypoint $x_i \in X$:

\begin{equation}
    \text{KL} [ \mathbb{N}(d_i, \hat{\sigma}_i) \| h_i(t) ],
\end{equation}

where $X$ is the set of all keypoints in an image for which the depth is known and $t$ is the far endpoint of the viewing ray. The variance $\hat{\sigma}_i$ is set to the uncertainty of the depth estimation for keypoint $x_i$. When depth is estimated with COLMAP, the uncertainty is calculated by re-projecting the keypoint to and from another camera position in which the keypoint is visible. In RGB-D data, however, the depth values are measurements rather than estimations. Therefore, we set $\hat{\sigma}_i = 1.0$ for all keypoints such that each depth value is weighted equally. We sample $10^5$ depth values in each ground truth image at random positions, where pixels that have a depth value equal to zero are never included.

\subsection{Dataset}
The 4D-OR dataset \cite{ozsoy20224dor} from the Technical University of Munich contains RGB-D images and camera poses from ten simulated knee replacement surgeries. We use this dataset to train a DS-NeRF in the reconstruction of five distinct phases in the surgery: ``empty OR'', ``patient in'', ``draping'', ``cleaning'' and ``procedure'' (see Figure~\ref{fig:phase_examples}). In this way, we can evaluate the quality of synthesised views for different OR activities.

The dataset contains synchronised images from six cameras that have fixed locations in the OR. Three of these cameras are located above the surgical field, each rotated approximately 90 degrees around the yaw axis (the red dots in Figure~\ref{fig:camera_poses}). Two of the three other cameras capture the OR from a wide perspective, while the sixth camera records from a position that is closer to the ground (the green dots in Figure~\ref{fig:camera_poses}).

\begin{figure}[t!]%
    \centering
    \includegraphics[width=\textwidth]{figures/phase_examples.png}
    \caption{Five distinct phases during or before the surgery. All images are obtained with the same camera.}
    \label{fig:phase_examples}
\end{figure}

\begin{figure}[t!]%
    \centering
    \includegraphics[width=0.6\textwidth]{figures/camera_poses.png}
    \caption{Locations of the RGB-D cameras are indicated by a red or green dot. The viewing angle is directed by the arrows. Red dots indicate three cameras located above the surgical field, whereas the green dots capture the OR from very different perspectives. The scene is a coloured point cloud formed by camera projection using depth values.}
    \label{fig:camera_poses}
\end{figure}

\subsection{Experimental Setup}
Our experiments are separated into two steps: a qualitative and quantitative analysis. In the qualitative step, we train DS-NeRF with three images from the cameras above the surgical field (the ``red'' cameras). After training, we instruct the algorithm to synthesise views from these exact poses as well as from interpolated poses that together form a 180 degrees rotation around the surgical field. In the quantitative step, we train DS-NeRF with five images captured by the camera positions that are not circled in Figure~\ref{fig:camera_poses}. At inference, the algorithm synthesises views from the remaining sixth position (the circled camera pose) which is unseen during training. We compare the resulting coloured images with ground truth images in terms of PSRN, SSIM \cite{wang2004image} and LPIPS \cite{zhang2018unreasonable}. Similarly, we evaluate the quality of depth perception in terms of mean absolute error (MAE) and in percentage of the ground truth depth value. Note that depth values equal to zero in the ground truth images are not included in this evaluation, since these values can be perceived as inaccurate measurements.

For all reconstructed scenes, DS-NeRF is trained to synthesise images with a resolution of $512 \times 384$ pixels with the following hyperparameters: 4096 selected rays per batch, 64 points sampled per ray, $5 \times 10^4$ iterations and depth loss weighting factor $\lambda_D$ set to 0.1.

\section{Results}

\subsection{Qualitative Analysis}

\begin{figure}
    \centering
    \includegraphics[width=\textwidth]{figures/nerf_results.png}
    \caption{DS-NeRF synthesised views for three phases in the OR where the virtual camera rotates 180 degrees around the surgical field. The top row displays the ground truth images for the starting camera pose. Views with a red border are generated from the camera poses with which the algorithm is trained, corresponding to the red camera positions in Figure~\ref{fig:camera_poses}.}
    \label{fig:nerf_results}
\end{figure}

The synthesised views for surgical phases ``empty OR'', ``patient in'' and ``procedure'' are given in Figure~\ref{fig:nerf_results}. When comparing the top-row synthesised views with the ground truth images, it can be seen that DS-NeRF is able to reconstruct the surgical scenes independent of surgical phase. Lighting conditions such as reflections on the floor and shadows are realistically rendered. However, the reconstructed scene looks smoothed with missing details, e.g. in the keyboard of the mobile monitor or the sterile clothing of the physician.

Synthesised views from the interpolated camera poses (images without red borders in Figure~\ref{fig:nerf_results}) correctly grasp the geometry of the scenes and realistically find the right lighting conditions. Nevertheless, the images do not look realistic due to a number of artefacts. One is the white background pixels that are rendered when DS-NeRF does not find any material density along viewing rays. These are present in the far corners of the OR. Second, a number of objects seem to be misaligned and occurring twice. For example, the tape on the floor and the instrument table are not always represented correctly. Surprisingly, this artefact seems to be less present in the ``procedure'' phase. Third, fine-grained details, such as the surgical instruments in the hands of the left physician, are missing to make the images convincingly realistic.

\subsection{Quantitative Analysis}
Results of the quantitative analysis can be found in Table~\ref{tab:results}. On average, DSNeRF is able to synthesise views from the unseen camera pose with 17.8 PSNR, 0.60 SIMM and 0.47 LPIPS. These results are comparable to the performance of the original NeRF on the NeRF Real dataset \cite{mildenhall2019local} when trained with 5 images: 18.2 PSNR, 0.57 SSIM and 0.50 LPIPS \cite{deng2022depth}. However, DSNeRF on the same dataset gains higher performance scores: 22.6 PSNR, 0.69 SSIM and 0.35 LPIPS. This indicates that our dataset is more challenging for the synthesis of high-quality images. The image quality of the rendered views on the 4D-OR dataset differs per phase and ranges in PSNR from 16.9 for ``patient in'' to 19.3 for ``empty OR''. This shows that the image quality is dependent on the complexity of the surgical scene.

\begin{table}[t!]
\begin{center}
\begin{minipage}{\textwidth}
\caption{Evaluation metrics comparing DS-NeRF synthesised views with unseen ground truth RGB-D images.}\label{tab:results}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lccccc@{\extracolsep{\fill}}}
    \toprule
    & \multicolumn{3}{@{}c@{}}{Colour Image} & \multicolumn{2}{@{}c@{}}{Depth Map} \\ \cmidrule{2-4} \cmidrule{5-6}
    Surgery phase & PSNR$\uparrow$ & SSIM$\uparrow$ & LPIPS$\downarrow$ & MAE (in cm)$\downarrow$ & Error (in \%)$\downarrow$\\
    \midrule
    Empty OR    & 19.3 & 0.71 & 0.44 & 2.3 & 0.97 \\
    Patient in  & 16.9 & 0.57 & 0.48 & 3.4 & 1.48 \\
    Draping     & 18.3 & 0.60 & 0.46 & 5.3 & 2.11 \\
    Cleaning    & 17.3 & 0.57 & 0.48 & 4.4 & 2.28 \\
    Procedure   & 17.3 & 0.57 & 0.50 & 5.8 & 3.67\\
    \textbf{Average} & \textbf{17.8} & \textbf{0.60} & \textbf{0.47} & \textbf{4.2} & \textbf{2.10} \\
    \bottomrule
\end{tabular*}
\end{minipage}
\end{center}
\end{table}

Table~\ref{tab:depth_results} displays the quality of the colour images and depth maps for NeRF with and without depth-supervision. The quality of the colour images decreases from 17.8 to 14.2 PSNR, while the error in depth estimation accuracy increases drastically from 4.2 to 56.2 cm. In terms of percentages, the depth error increases from 2.10 to 23.35 \%. These results show that depth-supervision helps NeRF to reconstruct the scene's 3D geometry accurately, resulting in a higher quality of synthesised images.

Figure~\ref{fig:depth_estimation} displays the estimated depth for an unseen camera position in the ``procedure'' phase in comparison with the ground truth depth channel captured from the same camera pose. It can be seen that DS-NeRF is able to grasp the geometry of the captured scene accurately. Moreover, the algorithm is able to generate depth values that are not present in the ground truth image due to the depth sensor's hexagon shape or sensor artefacts (e.g. the zero-valued ``shadows'').

\begin{table}[t!]
\begin{center}
\begin{minipage}{\textwidth}
\caption{Evaluation metrics for NeRF synthesised views with and without depth-supervision.}\label{tab:depth_results}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}cccccc@{\extracolsep{\fill}}}
    \toprule
    & \multicolumn{3}{@{}c@{}}{Colour Image} & \multicolumn{2}{@{}c@{}}{Depth Map} \\ \cmidrule{2-4} \cmidrule{5-6}
    Depth-supervision & PSNR$\uparrow$ & SSIM$\uparrow$ & LPIPS$\downarrow$ & MAE (in cm)$\downarrow$ & Error (in \%)$\downarrow$\\
    \midrule
    \checkmark & \textbf{17.8} & \textbf{0.60} & \textbf{0.47} & \textbf{4.2} & \textbf{2.10} \\
    $\times$ & 14.2 & 0.50 & 0.64 & 56.2 & 23.35 \\
    \bottomrule
\end{tabular*}
\end{minipage}
\end{center}
\end{table}

\begin{figure}[t!]%
    \centering
    \includegraphics[width=0.9\textwidth]{figures/depth_estimation.png}
    \caption{Example depth estimation output of DS-NeRF for the ``procedure'' phase (right) in comparison with the ground truth depth channel (left). Color bar displays distance in cm.}
    \label{fig:depth_estimation}
\end{figure}

\section{Discussion}
In this work, we explored the use of Neural Radiance Fields (NeRF) \cite{mildenhall2020nerf} for reconstructing surgical scenes in the operating room (OR) with multi-view RGB-D images from the 4D-OR dataset \cite{ozsoy20224dor}. We showed that the application of an original NeRF does not provide optimal reconstruction results and that the use of depth-supervision benefits the quality of the synthesised views. Depth-supervised NeRF (DS-NeRF) \cite{deng2022depth} removes the necessity to train the algorithm with tens to hundreds of camera positions, which are difficult to obtain during a surgical procedure.

Visual inspection of synthesised views around the surgical field showed that DS-NeRF is able to generate realistic images from the camera poses that the algorithm is trained with. Additionally, it is possible to use the technology to virtually rotate around the surgical field while the synthesised images remain geometrically consistent. However, the synthesised views from unseen camera poses miss fine details and contain artefacts that make the images look unrealistic. Training with more camera positions, larger image resolutions or stronger geometric priors can potentially help the algorithm produce views with higher quality.

The quantitative evaluation of DS-NeRF in generating views from an unseen camera position finds that the algorithm can produce views with a PSNR of 17.8. In comparison, DS-NeRF could generate views with larger image quality on the NeRF Real and the Redwood-3dscan datasets \cite{deng2022depth}. The performance difference can be explained by the distinct camera poses in the 4D-OR dataset, making the dataset more challenging for view synthesis. On the contrary, we found that DS-NeRF is able to find accurate depth maps for unseen camera poses, with an average depth error of 2.10\%.

We envision several potential uses for NeRF in the synthesis of OR images. The technology could be used for rendering virtual environments displaying real surgeries in 3D. With the current state of NeRF, where the rendering process is time-consuming, the most obvious use is for post-surgery rendering, where videos display the surgery from angles where no camera was originally positioned. In the long term, when NeRF rendering becomes cheaper, one could think of more interactive ways of experiencing a surgical procedure, either during or post-surgery, where the user could choose camera position, angle and zoom. The virtual renders could be static moments in a procedure, like ``snapshots'', or could display the surgery over time.

Besides improving the quality of view synthesises, there are other developments that could increase the impact of NeRF for 3D reconstruction in the OR. One is the synthesis of video instead of static images, which is shown to be possible \cite{li2022neural}. The time dimension can put an additional constraint on the training of NeRF, which is likely to benefit the rendering quality. More importantly, the synthesis of video would make NeRF more interesting for the development of virtual training applications. Another development is the drastic speedup in the training and rendering of NeRF algorithms. For example, \cite{mueller2022instant} have shown that it is possible to train high-quality neural graphics in seconds rather than minutes to hours. Last, the implicit 3D representation of the surgical scene could be used for further processing. For example, methods that use 3D representations for detecting human poses \cite{gerats20223d} have a potential benefit in using NeRF representations of humans in the OR, especially when NeRF is fitted to videos. Other video processing tasks, such as background removal, object detection and segmentation could potentially benefit similarly.

In conclusion, depth-supervised NeRF is able to synthesise views of the surgical field from OR images in which the 3D geometry is captured accurately. To reveal the full potential of NeRF for OR view synthesis, there remain several developments, such as video synthesis, training speedups and the use of implicit representations for downstream video processing tasks, that require further exploration.

\section*{Declarations}
Research at the Centre for Artificial Intelligence at Meander Medisch Centrum is sponsored by Johnson \& Johnson, Ltd. Jelmer M. Wolterink was supported by NWO domain Applied and Engineering Sciences VENI grant (18192).

GitHub projects with the DS-NeRF code implementation \cite{deng2022depth} and instructions for downloading the 4D-OR dataset \cite{ozsoy20224dor} are available publicly online.

\bibliographystyle{splncs04}

\section{Introduction}
The presentation of a novel approach for view synthesis called Neural Radiance Fields (NeRF) \cite{mildenhall2020nerf} caused an explosion of interest in the field of computer vision. Even though the original paper was presented recently, a large number of follow-up studies have already been published \cite{xie2022neural}. However, NeRF-based methods for clinical use remain largely unexplored. At the same time, there is increasing interest in virtual presence in operating rooms (ORs) during real or simulated surgeries. For example, the National Autonomous University of Mexico used virtual reality to simulate an OR, including distractions and interruptions, to train paediatric surgical residents during the COVID-19 pandemic \cite{perez2020immersive}. Apart from surgical training with virtual reality \cite{seymour2008vr}, physician assistant students can greatly benefit from training in a virtual environment \cite{francis2020operating}.

NeRF is a powerful technology for the reconstruction of a 3D scene from a set of images that capture the scene from various camera positions. Likewise, this technology could be used to build 3D representations of clinical environments such as the OR. NeRF requires only a set of calibrated cameras that capture the scene of interest and does not depend on any physical marker or complex sensory system. When applied to overhead cameras in the OR, NeRF could build 3D reconstructions of the surgical environment, providing the ability to render videos that virtually record surgical scenes. These videos could be used for virtual presence, helping students or clinicians to experience a surgery without the need to be actually present. The advantage over the existing systems for virtual presence in the OR, such as the ones mentioned above, is that NeRF can provide real instead of simulated surgeries.

In this paper, we show how NeRF can be used for view synthesis in the OR.  We show that depth-supervision \cite{deng2022depth} helps to increase the render quality and reduces the need for many camera positions. This is particularly relevant for clinical environments, where it is generally impossible to capture the scene with tens to hundreds of cameras.  In fact, we find that a depth-supervised NeRF with only three or five synchronised camera views captures the surgical field, and is able to generate images of the surgical intervention from a range of camera angles. In contrast to existing depth-supervision in NeRF, we directly optimise our model using  measured RGB-D sensor data instead of estimated depth from a Structure from Motion (SfM) algorithm.

\section{Related work}

\subsection{Neural Radiance Fields}
NeRF is a method for volume rendering, based upon the \textit{implicit representation} of a 3D scene in the weights of a neural network $F_\Theta$ \cite{mildenhall2020nerf}. This network is generally a standard multi-layer perceptron (MLP) that takes a 5D vector $(x, y, z, \theta, \phi)$ as input and that outputs a 4D vector $(RGB, \sigma)$. An input vector consists of a 3D location $(x, y, z)$ in the captured scene and an orientation $(\theta, \phi)$ from which this location is viewed. $F_\Theta$ returns for each vector a colour $RGB$ and a volume density $\sigma$. With this simple setup, NeRF can reconstruct images by casting a viewing ray from each pixel, sampling points along that ray, asking the MLP to find the colours and densities for these points and to sum over these results. In this way, it is possible to use a discrete set of sampled points in the 3D scene, while representing the 3D scene in continuous form. Reconstructed images are compared with ground truth images that are taken from the same camera positions. Importantly, the rendering function that sums over the found colours and densities is differentiable such that the MLP can be optimised by stochastic gradient descent. The loss function is often a total squared error between the colours of the rendered and the ground truth images.

\subsection{NeRF with Depth Priors}
Although the original NeRF has the ability to synthesise photo-realistic images from unseen camera perspectives, there are some limitations. One is that NeRF does not guarantee to capture 3D geometry accurately, which appears to be problematic for poorly textured areas that often occur in indoor scenes \cite{wei2021nerfingmvs}. Additionally, points are randomly sampled along a viewing ray, even though most of these points will describe empty space. It is likely that these problems will play a role when NeRF is applied to scenes in the OR, as these involve a large indoor environment.

Several solutions are proposed that enforce NeRF to find a more accurate geometry by regularisation with depth priors. Nerfing MVS \cite{wei2021nerfingmvs} provides a guided optimisation scheme for NeRF, where points are sampled along a viewing ray only around depth values found earlier. A sparse set of depth values is found by applying the COLMAP SfM algorithm \cite{schonberger2016structure} on the multi-view images. The sparse sets are used to train a depth completion network that provides full sets of depth values. With this optimisation scheme, NeRF is able to provide more accurate depth maps and has a better understanding of the scene's 3D geometry. \cite{neff2021donerf} have shown that computational costs at inference can be reduced significantly when conditioning NeRF on depth information. Their method involves another sampling strategy to include only points located around surfaces. These point locations are predicted by an oracle network.

\cite{roessle2022depthpriorsnerf} present a similar approach to leverage depth priors with depth-guided sampling. Additionally, the authors propose to add a loss term that enforces NeRF to terminate rays close to the most certain depth observations that are provided by a depth completion network. The work by \cite{rematas2022urban} shows how a depth-constrained NeRF is able to reconstruct large urban areas by training the network with an additional loss term as well. The loss enforces NeRF to represent a large amount of volume density around ground truth depth values found with a LiDAR sensor and a small amount in the area along the viewing ray that is closer to the camera. The depth-supervised NeRF \cite{deng2022depth} uses an additional loss function that operates with known depth values from RGB-D data or that are obtained from the COLMAP algorithm. This loss constraints the distribution of ray terminations to be similar to the known depth distribution by minimising the KL divergence between the two. The key insight is that they consider the uncertainty of the known depth values and constrain NeRF proportionally to the uncertainty.

The work above shows that depth priors help to reduce the number of camera poses required for NeRF to synthesise high-quality images. This is particularly relevant for the OR, where it is not possible to put cameras at all locations and the overall number of available cameras is limited.

\subsection{NeRF for Clinical Interventions}
Although NeRF has not been widely adopted in the field of computer-assisted interventions, the technology has been used for 3D reconstruction of soft tissues in robotic surgery videos by \cite{wang2022neural}. Because the laparoscopic view is a single view, their method uses time-dependent modelling of neural radiance and displacement fields, based upon D-NeRF \cite{pumarola2021d}. Using the stereoscopic camera of the surgical robot, the method finds depth maps along the coloured image frames. The depth information is used to constrain NeRF optimisation with an additional loss function.

\section{Methods}

\subsection{Depth-Supervised NeRF}
We use the depth-supervised NeRF (DS-NeRF) by \cite{deng2022depth} for building 3D reconstructions of OR scenes. This method regularises the training with an additional depth loss such that a model can be optimised with relatively few camera positions. The key idea in DS-NeRF is that most viewing rays terminate at the closest surface, which is often opaque. Therefore, most volume density should be found close to the distance of this surface along the viewing ray. DS-NeRF enforces such a distribution of volume density by minimising the KL divergence between the volume density distribution $h_i(t)$ and a normal distribution around the ground truth depth $d_i$ of keypoint $x_i \in X$:

\begin{equation}
    \text{KL} [ \mathbb{N}(d_i, \hat{\sigma}_i) \| h_i(t) ],
\end{equation}

where $X$ is the set of all keypoints in an image for which the depth is known and $t$ is the far endpoint of the viewing ray. The variance $\hat{\sigma}_i$ is set to the uncertainty of the depth estimation for keypoint $x_i$. When depth is estimated with COLMAP, the uncertainty is calculated by re-projecting the keypoint to and from another camera position in which the keypoint is visible. In RGB-D data, however, the depth values are measurements rather than estimations. Therefore, we set $\hat{\sigma}_i = 1.0$ for all keypoints such that each depth value is weighted equally. We sample $10^5$ depth values in each ground truth image at random positions, where pixels that have a depth value equal to zero are never included.

\subsection{Dataset}
The 4D-OR dataset \cite{ozsoy20224dor} from the Technical University of Munich contains RGB-D images and camera poses from ten simulated knee replacement surgeries. We use this dataset to train a DS-NeRF in the reconstruction of five distinct phases in the surgery: ``empty OR'', ``patient in'', ``draping'', ``cleaning'' and ``procedure'' (see Figure~\ref{fig:phase_examples}). In this way, we can evaluate the quality of synthesised views for different OR activities.

The dataset contains synchronised images from six cameras that have fixed locations in the OR. Three of these cameras are located above the surgical field, each rotated approximately 90 degrees around the yaw axis (the red dots in Figure~\ref{fig:camera_poses}). Two of the three other cameras capture the OR from a wide perspective, while the sixth camera records from a position that is closer to the ground (the green dots in Figure~\ref{fig:camera_poses}).

\begin{figure}[t!]%
    \centering
    \includegraphics[width=\textwidth]{figures/phase_examples.png}
    \caption{Five distinct phases during or before the surgery. All images are obtained with the same camera.}
    \label{fig:phase_examples}
\end{figure}

\begin{figure}[t!]%
    \centering
    \includegraphics[width=0.6\textwidth]{figures/camera_poses.png}
    \caption{Locations of the RGB-D cameras are indicated by a red or green dot. The viewing angle is directed by the arrows. Red dots indicate three cameras located above the surgical field, whereas the green dots capture the OR from very different perspectives. The scene is a coloured point cloud formed by camera projection using depth values.}
    \label{fig:camera_poses}
\end{figure}

\subsection{Experimental Setup}
Our experiments are separated into two steps: a qualitative and quantitative analysis. In the qualitative step, we train DS-NeRF with three images from the cameras above the surgical field (the ``red'' cameras). After training, we instruct the algorithm to synthesise views from these exact poses as well as from interpolated poses that together form a 180 degrees rotation around the surgical field. In the quantitative step, we train DS-NeRF with five images captured by the camera positions that are not circled in Figure~\ref{fig:camera_poses}. At inference, the algorithm synthesises views from the remaining sixth position (the circled camera pose) which is unseen during training. We compare the resulting coloured images with ground truth images in terms of PSRN, SSIM \cite{wang2004image} and LPIPS \cite{zhang2018unreasonable}. Similarly, we evaluate the quality of depth perception in terms of mean absolute error (MAE) and in percentage of the ground truth depth value. Note that depth values equal to zero in the ground truth images are not included in this evaluation, since these values can be perceived as inaccurate measurements.

For all reconstructed scenes, DS-NeRF is trained to synthesise images with a resolution of $512 \times 384$ pixels with the following hyperparameters: 4096 selected rays per batch, 64 points sampled per ray, $5 \times 10^4$ iterations and depth loss weighting factor $\lambda_D$ set to 0.1.

\section{Results}

\subsection{Qualitative Analysis}

\begin{figure}
    \centering
    \includegraphics[width=\textwidth]{figures/nerf_results.png}
    \caption{DS-NeRF synthesised views for three phases in the OR where the virtual camera rotates 180 degrees around the surgical field. The top row displays the ground truth images for the starting camera pose. Views with a red border are generated from the camera poses with which the algorithm is trained, corresponding to the red camera positions in Figure~\ref{fig:camera_poses}.}
    \label{fig:nerf_results}
\end{figure}

The synthesised views for surgical phases ``empty OR'', ``patient in'' and ``procedure'' are given in Figure~\ref{fig:nerf_results}. When comparing the top-row synthesised views with the ground truth images, it can be seen that DS-NeRF is able to reconstruct the surgical scenes independent of surgical phase. Lighting conditions such as reflections on the floor and shadows are realistically rendered. However, the reconstructed scene looks smoothed with missing details, e.g. in the keyboard of the mobile monitor or the sterile clothing of the physician.

Synthesised views from the interpolated camera poses (images without red borders in Figure~\ref{fig:nerf_results}) correctly grasp the geometry of the scenes and realistically find the right lighting conditions. Nevertheless, the images do not look realistic due to a number of artefacts. One is the white background pixels that are rendered when DS-NeRF does not find any material density along viewing rays. These are present in the far corners of the OR. Second, a number of objects seem to be misaligned and occurring twice. For example, the tape on the floor and the instrument table are not always represented correctly. Surprisingly, this artefact seems to be less present in the ``procedure'' phase. Third, fine-grained details, such as the surgical instruments in the hands of the left physician, are missing to make the images convincingly realistic.

\subsection{Quantitative Analysis}
Results of the quantitative analysis can be found in Table~\ref{tab:results}. On average, DSNeRF is able to synthesise views from the unseen camera pose with 17.8 PSNR, 0.60 SIMM and 0.47 LPIPS. These results are comparable to the performance of the original NeRF on the NeRF Real dataset \cite{mildenhall2019local} when trained with 5 images: 18.2 PSNR, 0.57 SSIM and 0.50 LPIPS \cite{deng2022depth}. However, DSNeRF on the same dataset gains higher performance scores: 22.6 PSNR, 0.69 SSIM and 0.35 LPIPS. This indicates that our dataset is more challenging for the synthesis of high-quality images. The image quality of the rendered views on the 4D-OR dataset differs per phase and ranges in PSNR from 16.9 for ``patient in'' to 19.3 for ``empty OR''. This shows that the image quality is dependent on the complexity of the surgical scene.

\begin{table}[t!]
\begin{center}
\begin{minipage}{\textwidth}
\caption{Evaluation metrics comparing DS-NeRF synthesised views with unseen ground truth RGB-D images.}\label{tab:results}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}lccccc@{\extracolsep{\fill}}}
    \toprule
    & \multicolumn{3}{@{}c@{}}{Colour Image} & \multicolumn{2}{@{}c@{}}{Depth Map} \\ \cmidrule{2-4} \cmidrule{5-6}
    Surgery phase & PSNR$\uparrow$ & SSIM$\uparrow$ & LPIPS$\downarrow$ & MAE (in cm)$\downarrow$ & Error (in \%)$\downarrow$\\
    \midrule
    Empty OR    & 19.3 & 0.71 & 0.44 & 2.3 & 0.97 \\
    Patient in  & 16.9 & 0.57 & 0.48 & 3.4 & 1.48 \\
    Draping     & 18.3 & 0.60 & 0.46 & 5.3 & 2.11 \\
    Cleaning    & 17.3 & 0.57 & 0.48 & 4.4 & 2.28 \\
    Procedure   & 17.3 & 0.57 & 0.50 & 5.8 & 3.67\\
    \textbf{Average} & \textbf{17.8} & \textbf{0.60} & \textbf{0.47} & \textbf{4.2} & \textbf{2.10} \\
    \bottomrule
\end{tabular*}
\end{minipage}
\end{center}
\end{table}

Table~\ref{tab:depth_results} displays the quality of the colour images and depth maps for NeRF with and without depth-supervision. The quality of the colour images decreases from 17.8 to 14.2 PSNR, while the error in depth estimation accuracy increases drastically from 4.2 to 56.2 cm. In terms of percentages, the depth error increases from 2.10 to 23.35 \%. These results show that depth-supervision helps NeRF to reconstruct the scene's 3D geometry accurately, resulting in a higher quality of synthesised images.

Figure~\ref{fig:depth_estimation} displays the estimated depth for an unseen camera position in the ``procedure'' phase in comparison with the ground truth depth channel captured from the same camera pose. It can be seen that DS-NeRF is able to grasp the geometry of the captured scene accurately. Moreover, the algorithm is able to generate depth values that are not present in the ground truth image due to the depth sensor's hexagon shape or sensor artefacts (e.g. the zero-valued ``shadows'').

\begin{table}[t!]
\begin{center}
\begin{minipage}{\textwidth}
\caption{Evaluation metrics for NeRF synthesised views with and without depth-supervision.}\label{tab:depth_results}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}cccccc@{\extracolsep{\fill}}}
    \toprule
    & \multicolumn{3}{@{}c@{}}{Colour Image} & \multicolumn{2}{@{}c@{}}{Depth Map} \\ \cmidrule{2-4} \cmidrule{5-6}
    Depth-supervision & PSNR$\uparrow$ & SSIM$\uparrow$ & LPIPS$\downarrow$ & MAE (in cm)$\downarrow$ & Error (in \%)$\downarrow$\\
    \midrule
    \checkmark & \textbf{17.8} & \textbf{0.60} & \textbf{0.47} & \textbf{4.2} & \textbf{2.10} \\
    $\times$ & 14.2 & 0.50 & 0.64 & 56.2 & 23.35 \\
    \bottomrule
\end{tabular*}
\end{minipage}
\end{center}
\end{table}

\begin{figure}[t!]%
    \centering
    \includegraphics[width=0.9\textwidth]{figures/depth_estimation.png}
    \caption{Example depth estimation output of DS-NeRF for the ``procedure'' phase (right) in comparison with the ground truth depth channel (left). Color bar displays distance in cm.}
    \label{fig:depth_estimation}
\end{figure}

\section{Discussion}
In this work, we explored the use of Neural Radiance Fields (NeRF) \cite{mildenhall2020nerf} for reconstructing surgical scenes in the operating room (OR) with multi-view RGB-D images from the 4D-OR dataset \cite{ozsoy20224dor}. We showed that the application of an original NeRF does not provide optimal reconstruction results and that the use of depth-supervision benefits the quality of the synthesised views. Depth-supervised NeRF (DS-NeRF) \cite{deng2022depth} removes the necessity to train the algorithm with tens to hundreds of camera positions, which are difficult to obtain during a surgical procedure.

Visual inspection of synthesised views around the surgical field showed that DS-NeRF is able to generate realistic images from the camera poses that the algorithm is trained with. Additionally, it is possible to use the technology to virtually rotate around the surgical field while the synthesised images remain geometrically consistent. However, the synthesised views from unseen camera poses miss fine details and contain artefacts that make the images look unrealistic. Training with more camera positions, larger image resolutions or stronger geometric priors can potentially help the algorithm produce views with higher quality.

The quantitative evaluation of DS-NeRF in generating views from an unseen camera position finds that the algorithm can produce views with a PSNR of 17.8. In comparison, DS-NeRF could generate views with larger image quality on the NeRF Real and the Redwood-3dscan datasets \cite{deng2022depth}. The performance difference can be explained by the distinct camera poses in the 4D-OR dataset, making the dataset more challenging for view synthesis. On the contrary, we found that DS-NeRF is able to find accurate depth maps for unseen camera poses, with an average depth error of 2.10\%.

We envision several potential uses for NeRF in the synthesis of OR images. The technology could be used for rendering virtual environments displaying real surgeries in 3D. With the current state of NeRF, where the rendering process is time-consuming, the most obvious use is for post-surgery rendering, where videos display the surgery from angles where no camera was originally positioned. In the long term, when NeRF rendering becomes cheaper, one could think of more interactive ways of experiencing a surgical procedure, either during or post-surgery, where the user could choose camera position, angle and zoom. The virtual renders could be static moments in a procedure, like ``snapshots'', or could display the surgery over time.

Besides improving the quality of view synthesises, there are other developments that could increase the impact of NeRF for 3D reconstruction in the OR. One is the synthesis of video instead of static images, which is shown to be possible \cite{li2022neural}. The time dimension can put an additional constraint on the training of NeRF, which is likely to benefit the rendering quality. More importantly, the synthesis of video would make NeRF more interesting for the development of virtual training applications. Another development is the drastic speedup in the training and rendering of NeRF algorithms. For example, \cite{mueller2022instant} have shown that it is possible to train high-quality neural graphics in seconds rather than minutes to hours. Last, the implicit 3D representation of the surgical scene could be used for further processing. For example, methods that use 3D representations for detecting human poses \cite{gerats20223d} have a potential benefit in using NeRF representations of humans in the OR, especially when NeRF is fitted to videos. Other video processing tasks, such as background removal, object detection and segmentation could potentially benefit similarly.

In conclusion, depth-supervised NeRF is able to synthesise views of the surgical field from OR images in which the 3D geometry is captured accurately. To reveal the full potential of NeRF for OR view synthesis, there remain several developments, such as video synthesis, training speedups and the use of implicit representations for downstream video processing tasks, that require further exploration.

\section*{Declarations}
Research at the Centre for Artificial Intelligence at Meander Medisch Centrum is sponsored by Johnson \& Johnson, Ltd. Jelmer M. Wolterink was supported by NWO domain Applied and Engineering Sciences VENI grant (18192).

GitHub projects with the DS-NeRF code implementation \cite{deng2022depth} and instructions for downloading the 4D-OR dataset \cite{ozsoy20224dor} are available publicly online.

\bibliographystyle{splncs04}

redpajama_set_name: RedPajamaArXiv


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text:
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text:
Q: Delete third element in F# list I am writing a function to return a list minus the third value.
Here is my current code:
let listString = [ "1"; "2"; "3"; "4" ];;

let del3 (listA :'a)  =  [listA.Head; listA.Tail.Head] @ [listA.Tail.Tail.Tail];;

del3 listString

and I am getting the error:

Lookup on object of indeterminate type based on information prior to this program point. A type annotation may be needed prior to this program point to constrain the type of the object. This may allow the lookup to be resolved.

What should I change to fix the error?

A: You need to let the compiler know that listA is a list. Also Tail returns a list, so for the second list you're appending you don't want to wrap the tail in a list, otherwise you're going to have a list of a list:
let listString = [ "1"; "2"; "3"; "4" ]

let del3 (listA :'a list)  =  [listA.Head; listA.Tail.Head] @ listA.Tail.Tail.Tail

del3 listString;;

A solution to handle lists of all sizes:
let del3 = function
    | a::b::c::tail -> a::b::tail
    | list -> list

A: When accessing members, methods or properties of an object, F# needs to know the type of that object. It can't just infer the type from the fact that you're accessing a property named Head because there might be many different classes that have such a property.
To fix this problem, either give listA a type annotation or use List.head and List.tail instead of the properties.

A: I think a simpler approach based on a pattern match might be better
let del3 = function |a::b::c::d -> a::b::d | _ -> failwith "insufficient input"

redpajama_set_name: RedPajamaStackExchange


text:
How to submit a letter
Readers React: There must be a better way to house homeless people now than by building $500,000 units
A row of tents in a homeless encampment lines South Beaudry Avenue in downtown Los Angeles on Nov. 17, 2017.
(Los Angeles Times)
Feb. 26, 2018 1:05 PM PT
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The good news is that Measure H, the county's quarter-cent sales tax hike passed in 2017, carves out some of the revenue it raises to cover rent subsidies for individuals who will receive social services while living in existing market-rate apartments.
Now it's up to my fellow landlords to step up and join me in accepting L.A. County homeless applicants in their buildings.
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The writer is chairman-elect of the California Apartment Assn. of Los Angeles.
To the editor: As an Angeleno for the last 15 years, I have witnessed firsthand the slow but staggering spread of misery and madness on our city's streets. It is an omnipresent, shameful stain on one of the most beautiful, vibrant cities in the world.
But you miss the mark when you say most of us are no longer either shocked or shamed. To some extent, we are all uncomfortable, irritated, disgusted, scared or oblivious. But mostly we are angry — not at homeless people, but at our elected officials, whose task it is to enact solutions to this solvable (yes, solvable) problem.
Voters in Los Angeles have decided to tax themselves to pay for more housing and services. We volunteer at shelters and donate clothes, food and money. We stay calm when screamed at by mentally ill people and vow patience when camps go up near our children's parks.
Our elected officials are far too calm, however. They need to establish large-scale temporary housing and services as if this were a refugee crisis. It is done in a matter of weeks in war zones across the globe.
Because the truth is Los Angeles is indeed under assault — not by the homeless, but by homelessness. And the quality of millions of lives is at stake.
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To the editor: Why can't we build housing based on college dormitories? It would be less expensive than building full apartment units and house more people much more quickly and at a lower cost.
This type of housing would be adaptable for those who need support services. Bathrooms and kitchens down the hall might not be optimal, but would at least provide access at decreased cost and be a heck of a lot better than living in tents on the street.
Reading about Los Angeles' city-owned parking lots as sites for housing, I would suggest this as an option for new building.
Susan Chorpenning, Altadena
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Home > Natural Cures/Hotlistic Living and Nutrition > Erin Brockovich "Why EPA Headquarters' Union of Scientists Opposes Fluoridation."
Erin Brockovich "Why EPA Headquarters' Union of Scientists Opposes Fluoridation."
Natural Cures/Hotlistic Living and Nutrition
by Nate Max - June 25, 2015 0
WHY EPA HEADQUARTERS UNION OF SCIENTISTS
OPPOSES FLUORIDATION
"Why EPA Headquarters' Union of Scientists Opposes Fluoridation."
The following documents why our union, formerly National Federation of Federal Employees Local 2050 and since April 1998 Chapter 280 of the National Treasury Employees Union, took the stand it did opposing fluoridation of drinking water supplies. Our union is comprised of and represents the approximately 1500 scientists, lawyers, engineers and other professional employees at EPA Headquarters here in Washington, D.C.
The union first became interested in this issue rather by accident. Like most Americans, including many physicians and dentists, most of our members had thought that fluoride's only effects were beneficial – reductions in tooth decay, etc. We too believed assurances of safety and effectiveness of water fluoridation.
Then, as EPA was engaged in revising its drinking water standard for fluoride in 1985, an employee came to the union with a complaint: he said he was being forced to write into the regulation a statement to the effect that EPA thought it was alright for children to have "funky" teeth. It was OK, EPA said, because it considered that condition to be only a cosmetic effect, not an adverse health effect. The reason for this EPA position was that it was under political pressure to set its health-based standard for fluoride at 4 mg/liter. At that level, EPA knew that a significant number of children develop moderate to severe dental fluorosis, but since it had deemed the effect as only cosmetic, EPA didn't have to set its health-based standard at a lower level to prevent it.
We tried to settle this ethics issue quietly, within the family, but EPA was unable or unwilling to resist external political pressure, and we took the fight public with a union amicus curiae brief in a lawsuit filed against EPA by a public interest group. The union has published on this initial involvement period in detail.\1
Since then our opposition to drinking water fluoridation has grown, based on the scientific literature documenting the increasingly out-of-control exposures to fluoride, the lack of benefit to dental health from ingestion of fluoride and the hazards to human health from such ingestion. These hazards include acute toxic hazard, such as to people with impaired kidney function, as well as chronic toxic hazards of gene mutations, cancer, reproductive effects, neurotoxicity, bone pathology and dental fluorosis. First, a review of recent neurotoxicity research results.
In 1995, Mullenix and co-workers \2 showed that rats given fluoride in drinking water at levels that give rise to plasma fluoride concentrations in the range seen in humans suffer neurotoxic effects that vary according to when the rats were given the fluoride – as adult animals, as young animals, or through the placenta before birth. Those exposed before birth were born hyperactive and remained so throughout their lives. Those exposed as young or adult animals displayed depressed activity. Then in 1998, Guan and co-workers \3 gave doses similar to those used by the Mullenix research group to try to understand the mechanism(s) underlying the effects seen by the Mullenix group. Guan's group found that several key chemicals in the brain – those that form the membrane of brain cells – were substantially depleted in rats given fluoride, as compared to those who did not get fluoride.
Another 1998 publication by Varner, Jensen and others \4 reported on the brain- and kidney damaging effects in rats that were given fluoride in drinking water at the same level deemed "optimal" by pro-fluoridation groups, namely 1 part per million (1 ppm). Even more pronounced damage was seen in animals that got the fluoride in conjunction with aluminum. These results are especially disturbing because of the low dose level of fluoride that shows the toxic effect in rats – rats are more resistant to fluoride than humans. This latter statement is based on Mullenix's finding that it takes substantially more fluoride in the drinking water of rats than of humans to reach the same fluoride level in plasma. It is the level in plasma that determines how much fluoride is "seen" by particular tissues in the body. So when rats get 1 ppm in drinking water, their brains and kidneys are exposed to much less fluoride than humans getting 1 ppm, yet they are experiencing toxic effects. Thus we are compelled to consider the likelihood that humans are experiencing damage to their brains and kidneys at the "optimal" level of 1 ppm.
In support of this concern are results from two epidemiology studies from China\5,\6 that show decreases in I.Q. in children who get more fluoride than the control groups of children in each study. These decreases are about 5 to 10 I.Q. points in children aged 8 to 13 years.
Another troubling brain effect has recently surfaced: fluoride's interference with the function of the brain's pineal gland. The pineal gland produces melatonin which, among other roles, mediates the body's internal clock, doing such things as governing the onset of puberty. Jennifer Luke\7 has shown that fluoride accumulates in the pineal gland and inhibits its production of melatonin. She showed in test animals that this inhibition causes an earlier onset of sexual maturity, an effect reported in humans as well in 1956, as part of the Kingston/Newburgh study, which is discussed below. In fluoridated Newburgh, young girls experienced earlier onset of menstruation (on average, by six months) than girls in non-fluoridated Kingston \8.
From a risk assessment perspective, all these brain effect data are particularly compelling and disturbing because they are convergent.
We looked at the cancer data with alarm as well. There are epidemiology studies that are convergent with whole-animal and single-cell studies (dealing with the cancer hazard), just as the neurotoxicity research just mentioned all points in the same direction. EPA fired the Office of Drinking Water's chief toxicologist, Dr. William Marcus, who also was our local union's treasurer at the time, for refusing to remain silent on the cancer risk issue\9 . The judge who heard the lawsuit he brought against EPA over the firing made that finding – that EPA fired him over his fluoride work and not for the phony reason put forward by EPA management at his dismissal. Dr. Marcus won his lawsuit and is again at work at EPA. Documentation is available on request.
The type of cancer of particular concern with fluoride, although not the only type, is osteosarcoma, especially in males. The National Toxicology Program conducted a two-year study \10 in which rats and mice were given sodium fluoride in drinking water. The positive result of that study (in which malignancies in tissues other than bone were also observed), particularly in male rats, is convergent with a host of data from tests showing fluoride's ability to cause mutations (a principal "trigger" mechanism for inducing a cell to become cancerous) e.g.\11a, b, c, d and data showing increases in osteosarcomas in young men in New Jersey \12 , Washington and Iowa \13 based on their drinking fluoridated water. It was his analysis, repeated statements about all these and other incriminating cancer data, and his requests for an independent, unbiased evaluation of them that got Dr. Marcus fired.
Bone pathology other than cancer is a concern as well. An excellent review of this issue was published by Diesendorf et al. in 1997 \14. Five epidemiology studies have shown a higher rate of hip fractures in fluoridated vs. non-fluoridated communities. \15a, b, c, d, e. Crippling skeletal fluorosis was the endpoint used by EPA to set its primary drinking water standard in 1986, and the ethical deficiencies in that standard setting process prompted our union to join the Natural Resources Defense Council in opposing the standard in court, as mentioned above.
Regarding the effectiveness of fluoride in reducing dental cavities, there has not been any double-blind study of fluoride's effectiveness as a caries preventative. There have been many, many small scale, selective publications on this issue that proponents cite to justify fluoridation, but the largest and most comprehensive study, one done by dentists trained by the National Institute of Dental Research, on over 39,000 school children aged 5-17 years, shows no significant differences (in terms of decayed, missing and filled teeth) among caries incidences in fluoridated, non-fluoridated and partially fluoridated communities.\16. The latest publication \17 on the fifty-year fluoridation experiment in two New York cities, Newburgh and Kingston, shows the same thing. The only significant difference in dental health between the two communities as a whole is that fluoridated Newburgh, N.Y. shows about twice the incidence of dental fluorosis (the first, visible sign of fluoride chronic toxicity) as seen in non-fluoridated Kingston.
John Colquhoun's publication on this point of efficacy is especially important\18. Dr. Colquhoun was Principal Dental Officer for Auckland, the largest city in New Zealand, and a staunch supporter of fluoridation – until he was given the task of looking at the world-wide data on fluoridation's effectiveness in preventing cavities. The paper is titled, "Why I changed My Mind About Water Fluoridation." In it Colquhoun provides details on how data were manipulated to support fluoridation in English speaking countries, especially the U.S. and New Zealand. This paper explains why an ethical public health professional was compelled to do a 180 degree turn on fluoridation.
Further on the point of the tide turning against drinking water fluoridation, statements are now coming from other dentists in the pro-fluoride camp who are starting to warn that topical fluoride (e.g. fluoride in tooth paste) is the only significantly beneficial way in which that substance affects dental health \19, \20, \21. However, if the concentrations of fluoride in the oral cavity are sufficient to inhibit bacterial enzymes and cause other bacteriostatic effects, then those concentrations are also capable of producing adverse effects in mammalian tissue, which likewise relies on enzyme systems. This statement is based not only on common sense, but also on results of mutation studies which show that fluoride can cause gene mutations in mammalian and lower order tissues at fluoride concentrations estimated to be present in the mouth from fluoridated tooth paste\22. Further, there were tumors of the oral cavity seen in the NTP cancer study mentioned above, further strengthening concern over the toxicity of topically applied fluoride.
In any event, a person can choose whether to use fluoridated tooth paste or not (although finding non-fluoridated kinds is getting harder and harder), but one cannot avoid fluoride when it is put into the public water supplies.
So, in addition to our concern over the toxicity of fluoride, we note the uncontrolled – and apparently uncontrollable – exposures to fluoride that are occurring nationwide via drinking water, processed foods, fluoride pesticide residues and dental care products. A recent report in the lay media\23, that, according to the Centers for Disease Control, at least 22 percent of America's children now have dental fluorosis, is just one indication of this uncontrolled, excess exposure. The finding of nearly 12 percent incidence of dental fluorosis among children in un-fluoridated Kingston New York\17 is another. For governmental and other organizations to continue to push for more exposure in the face of current levels of over-exposure coupled with an increasing crescendo of adverse toxicity findings is irrational and irresponsible at best.
Thus, we took the stand that a policy which makes the public water supply a vehicle for disseminating this toxic and prophylactically useless (via ingestion, at any rate) substance is wrong.
We have also taken a direct step to protect the employees we represent from the risks of drinking fluoridated water. We applied EPA's risk control methodology, the Reference Dose, to the recent neurotoxicity data. The Reference Dose is the daily dose, expressed in milligrams of chemical per kilogram of body weight, that a person can receive over the long term with reasonable assurance of safety from adverse effects. Application of this methodology to the Varner et al.\4 data leads to a Reference Dose for fluoride of 0.000007 mg/kg-day. Persons who drink about one quart of fluoridated water from the public drinking water supply of the District of Columbia while at work receive about 0.01mg/kg-day from that source alone. This amount of fluoride is more than 100 times the Reference Dose. On the basis of these results the union filed a grievance, asking that EPA provide un-fluoridated drinking water to its employees.
The implication for the general public of these calculations is clear. Recent, peer-reviewed toxicity data, when applied to EPA's standard method for controlling risks from toxic chemicals, require an immediate halt to the use of the nation's drinking water reservoirs as disposal sites for the toxic waste of the phosphate fertilizer industry\24.
END NOTE LITERATURE CITATIONS
1.Applying the NAEP code of ethics to the Environmental Protection Agency and the fluoride in drinking water standard. Carton, R.J. and Hirzy, J.W. Proceedings of the 23rd Ann. Conf. of the National Association of Environmental Professionals. 20-24 June, 1998. GEN 51-61.
2.Neurotoxicity of sodium fluoride in rats. Mullenix, P.J., Denbesten, P.K., Schunior, A. and Kernan, W.J. Neurotoxicol. Teratol. 17 169-177 (1995)
3. Influence of chronic fluorosis on membrane lipids in rat brain. Z.Z. Guan, Y.N. Wang, K.Q. Xiao, D.Y. Dai, Y.H. Chen, J.L. Liu, P. Sindelar and G. Dallner, Neurotoxicology and Teratology 20 537-542 (1998).
4. Chronic administration of aluminum- fluoride or sodium-fluoride to rats in drinking water: alterations in neuronal and cerebrovascular integrity. Varner, J.A., Jensen, K.F., Horvath, W. And Isaacson, R.L. Brain Research 784 284-298 (1998).
5. Effect of high fluoride water supply on children's intelligence. Zhao, L.B., Liang, G.H., Zhang, D.N., and Wu, X.R. Fluoride 29 190-192 (1996)
6.. Effect of fluoride exposure on intelligence in children. Li, X.S., Zhi, J.L., and Gao, R.O. Fluoride 28 (1995). 7. Effect of fluoride on the physiology of the pineal gland. Luke, J.A. Caries Research 28 204 (1994).
8. Newburgh-Kingston caries-fluorine study XIII. Pediatric findings after ten years. Schlesinger, E.R., Overton, D.E., Chase, H.C., and Cantwell, K.T. JADA 52 296-306 (1956).
9. Memorandum dated May 1, 1990. Subject: Fluoride Conference to Review the NTP Draft Fluoride Report; From: Wm. L. Marcus, Senior Science Advisor ODW; To: Alan B. Hais, Acting Director Criteria & Standards Division ODW.
10. Toxicology and carcinogenesis studies of sodium fluoride in F344/N rats and B6C3F1 mice. NTP Report No. 393 (1991).
11a. Chromosome aberrations, sister chromatid exchanges, unscheduled DNA synthesis and morphological neoplastic transformation in Syrian hamster embryo cells. Tsutsui et al. Cancer Research 44 938-941 (1984).
11b. Cytotoxicity, chromosome aberrations and unscheduled DNA synthesis in cultured human diploid fibroblasts. Tsutsui et al. Mutation Research 139 193-198 (1984).
11c. Positive mouse lymphoma assay with and without S-9 activation; positive sister chromatid exchange in Chinese hamster ovary cells with and without S-9 activation; positive chromosome aberration without S-9 activation. Toxicology and carcinogenesis studies of sodium fluoride in F344/N rats and B6C3F1 mice. NTP Report No. 393 (1991).
11d. An increase in the number of Down's syndrome babies born to younger mothers in cities following fluoridation. Science and Public Policy 12 36-46 (1985).
12. A brief report on the association of drinking water fluoridation and the incidence of osteosarcoma among young males. Cohn, P.D. New Jersey Department of Health (1992).
13. Surveillance, epidemiology and end results (SEER) program. National Cancer Institute in Review of fluoride benefits and risks. Department of Health and Human Services. F1-F7 (1991).
14. New evidence on fluoridation. Diesendorf, M., Colquhoun, J., Spittle, B.J., Everingham, D.N., and Clutterbuck, F.W. Australian and New Zealand J. Public Health. 21 187-190 (1997).
15a. Regional variation in the incidence of hip fracture: U.S. white women aged 65 years and older. Jacobsen, S.J., Goldberg, J., Miles, ,T.P. et al. JAMA 264 500-502 (1990)
15b. Hip fracture and fluoridation in Utah's elderly population. Danielson, C., Lyon, J.L., Egger, M., and Goodenough, G.K. JAMA 268 746-748 (1992).
15c. The association between water fluoridation and hip fracture among white women and men aged 65 years and older: a national ecological study. Jacobsen, S.J., Goldberg, J., Cooper, C. and Lockwood, S.A. Ann. Epidemiol.2 617-626 (1992).
15d. Fluorine concentration is drinking water and fractures in the elderly [letter]. Jacqmin-Gadda, H., Commenges, D. and Dartigues, J.F. JAMA 273 775-776 (1995).
15e. Water fluoridation and hip fracture [letter]. Cooper, C., Wickham, C.A.C., Barker, D.J.R. and Jacobson, S.J. JAMA 266 513-514 (1991).
16. Water fluoridation and tooth decay: Results from the 1986-1987 national survey of U.S. school children. Yiamouyannis, J. Fluoride 23 55-67 (1990).
17. Recommendations for fluoride use in children. Kumar, J.V. and Green, E.L. New York State Dent. J. (1998) 40-47.
18. Why I changed my mind about water fluoridation. Colquhoun, J. Perspectives in Biol. And Medicine 41 1-16 (1997).
19. A re-examination of the pre-eruptive and post-eruptive mechanism of the anti-caries effects of fluoride: is there any anti-caries benefit from swallowing fluoride? Limeback, H. Community Dent. Oral Epidemiol. 27 62-71 (1999).
20. Fluoride supplements for young children: an analysis of the literature focussing on benefits and risks. Riordan, P.J. Community Dent. Oral Epidemiol. 27 72-83 (1999).
21. Prevention and reversal of dental caries: role of low level fluoride. Featherstone, J.D. Community Dent. Oral Epidemiol. 27 31-40 (1999).
22. Appendix H. Review of fluoride benefits and risks. Department of Health and Human Services. H1-H6 (1991).
23.Some young children get too much fluoride. Parker-Pope, T. Wall Street Journal Dec. 21, 1998.
24. Letter from Rebecca Hanmer, Deputy Assistant Administrator for Water, to Leslie Russell re: EPA view on use of by-product fluosilicic (sic) acid as low cost source of fluoride to water authorities. March 30, 1983.
OTHER CITATIONS (This short list does not include the entire literature on fluoride effects)
a. Exposure to high fluoride concentrations in drinking water is associated with decreased birth rates. Freni, S.C. J. Toxicol. Environ. Health 42 109-121 (1994)
b. Ameliorative effects of reduced food-borne fluoride on reproduction in silver foxes. Eckerlin, R.H., Maylin, G.A., Krook, L., and Carmichael, D.T. Cornell Vet. 78 75-91 (1988).
c. Milk production of cows fed fluoride contaminated commercial feed. Eckerlin, R.H., Maylin, G.A., and Krook, L. Cornell Vet. 76 403-404 (1986).
d. Maternal-fetal transfer of fluoride in pregnant women. Calders, R., Chavine, J., Fermanian, J., Tortrat, D., and Laurent, A.M. Biol. Neonate 54 263-269 (1988).
e. Effects of fluoride on screech owl reproduction: teratological evaluation, growth, and blood chemistry in hatchlings. Hoffman, D.J., Pattee, O.H., and Wiemeyer, S.N. Toxicol. Lett. 26 19-24 (1985).
f. Fluoride intoxication in dairy calves. Maylin, G.A., Eckerlin, R.H., and Krook, L. Cornell Vet. 77 84-98 (1987).
g. Fluoride inhibition of protein synthesis. Holland, R.I. Cell Biol. Int. Rep. 3 701-705 (1979).
h. An unexpectedly strong hydrogen bond: ab initio calculations and spectroscopic studies of amide-fluoride systems. Emsley, J., Jones, D.J., Miller, J.M., Overill, R.E. and Waddilove, R.A. J. Am. Chem. Soc. 103 24-28 (1981).
i. The effect of sodium fluoride on the growth and differentiation of human fetal osteoblasts. Song, X.D., Zhang, W.Z., Li, L.Y., Pang, Z.L., and Tan, Y.B. Fluoride 21 149-158 (1988).
j. Modulation of phosphoinositide hydrolysis by NaF and aluminum in rat cortical slices. Jope, R.S. J. Neurochem. 51 1731-1736 (1988).
k. The crystal structure of fluoride-inhibited cytochrome c peroxidase. Edwards, S.L., Poulos, T.L., Kraut, J. J. Biol. Chem. 259 12984-12988 (1984).
l. Intracellular fluoride alters the kinetic properties of calcium currents facilitating the investigation of synaptic events in hippocampal neurons. Kay, A.R., Miles, R., and Wong, R.K.S. J. Neurosci. 6 2915-2920 (1986).
m. Fluoride intoxication: a clinical-hygienic study with a review of the literature and some experimental investigations. Roholm, K. H.K. Lewis Ltd (London) (1937).
n. Toxin-induced blood vessel inclusions caused by the chronic administration of aluminum and sodium fluoride and their implications for dementia. Isaacson, R.L., Varner, J.A., and Jensen, K. F. Ann. N.Y. Acad. Sci. 825 152-166 (1997).
o. Allergy and hypersensitivity to fluoride. Spittle, B. Fluoride 26 267-273 (1993)
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text:
#ifndef REALM_UTIL_TERMINATE_HPP
#define REALM_UTIL_TERMINATE_HPP

#include <cstdlib>
#include <sstream>

#include <realm/util/features.h>
#include <realm/util/inspect.hpp>
#include <realm/version.hpp>

#define REALM_TERMINATE(msg) realm::util::terminate((msg), __FILE__, __LINE__)

namespace realm {
namespace util {

/// Install a custom termination notification callback. This will only be called as a result of
/// Realm crashing internally, i.e. a failed assertion or an otherwise irrecoverable error
/// condition. The termination notification callback is supplied with a zero-terminated string
/// containing information relevant for debugging the issue leading to the crash.
///
/// The termination notification callback is shared by all threads, which is another way of saying
/// that it must be reentrant, in case multiple threads crash simultaneously.
///
/// Furthermore, the provided callback must be `noexcept`, indicating that if an exception
/// is thrown in the callback, the process is terminated with a call to `std::terminate`.
void set_termination_notification_callback(void(*callback)(const char* message) noexcept) noexcept;

REALM_NORETURN void terminate_internal(std::stringstream&) noexcept;

REALM_NORETURN void terminate(const char* message, const char* file, long line) noexcept;

// LCOV_EXCL_START
template<class... Ts>
REALM_NORETURN void terminate(const char* message, const char* file, long line,
                              Ts... infos) noexcept
{
    std::stringstream ss;
    static_assert(sizeof...(infos) == 2 || sizeof...(infos) == 4 || sizeof...(infos) == 6,
                  "Called realm::util::terminate() with wrong number of arguments");
    ss << file << ':' << line << ": " REALM_VER_CHUNK " " << message << " [";
    inspect_all(ss, std::forward<Ts>(infos)...);
    ss << "]" << '\n';

    terminate_internal(ss);
}
// LCOV_EXCL_STOP

template<class... Args>
REALM_NORETURN void terminate_with_info(const char* assert_message, int line, const char* file,
                                        const char* interesting_names,
                                        Args&&... interesting_values) noexcept
{
    std::stringstream ss;
    ss << file << ':' << line << ": " REALM_VER_CHUNK " ";
    ss << assert_message << " with " << interesting_names << " = (";
    inspect_all(ss, std::forward<Args>(interesting_values)...);
    ss << "). \n";
    terminate_internal(ss);
}

} // namespace util
} // namespace realm

#endif // REALM_UTIL_TERMINATE_HPP

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