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Q: What are the shiny circles on Thor's costume?
Anyone have any idea what they are or what they're for?
I'll take a Marvel Universe explanation or even a Norse mythology answer. Thank you!

A: This answer'slinks are mostly conjecture and fan theories. I have some canon material, but I lacked to find anything solid.
It appears if they are just for protection(theory), also on a lesser note they appear to keep his cape on(in some designs).
My theory that they were for protection and were also symbols of his honor and status is shown when Odin rips them off and tells him that he is not worthy of his friends and of his title.
Gotten from this source.

[Incensed about Thor and the Warriors Three's mission to Jotunheim, Odin brings them back to Asgard]
Thor: Why did you bring us back?
Odin: Do you realize what you've done? What you've started?
Thor: I was protecting my home.
Odin: You cannot even protect your friends! How can you hope to protect a kingdom? [speaking to Heimdall] Get him to a healing room! Now!
Thor: There won't be a kingdom to protect if you're afraid to act. The Jotuns must learn to fear me, just as they once feared you.
Odin: That's pride and vanity talking, not leadership. You've forgotten everything I taught you about a warrior's patience.
Thor: While you wait and be patient, The Nine Realms laugh at us. The old ways are done. You'd stand giving speeches while Asgard falls.
Odin: You are a vain, greedy, cruel boy!
Thor: And you are an old man and a fool!
Odin: Yes. I was a fool to think you were ready.
Loki: Father...
Odin: [to Loki] HEY! [to Thor] Thor Odinson, you have betrayed the express command of your king. Through your arrogance and stupidity, you have opened these peaceful realms and innocent lives to the horror and desolation of war! You are unworthy of these realms!  You're unworthy of your TITLE! YOU'RE UNWORTHY!.. of the loved ones you have betrayed. I now take from you your power! In the name of my father and his father before, I, Odin Allfather, CAST YOU OUT! [banishes Thor to Earth] Whosoever holds this hammer, if he be worthy, shall possess the power of Thor. [throws Mjolnir to Earth]

I do not put much into the theory that they are for protection as Thor has his belt and hammer for protection. Also, if I remember correctly the disks have things hit it and are reflected or the lessen the impact, so they might have some protective qualities.
This is a forum that explains that, but it is fan talk(so beware).
Other notes:
Thor's armor was an amalgamation of the versions seen in both the original Marvel and the "Ultimate Marvel" comics.
From marvel.com:

Thor wears a full body hauberk composed of Asgardian steel. It belt
  has the Norse symbol of physical health as a belt buckle along with
  the Norse symbol of Gemini most likely to symbolize his bond with Dr.
  Donald Blake.

This is from reddit:

As you probably saw in the Thor movie, Odin rips them off of Thor when he is banished to Earth and his armor disintegrates. The six of them compromise Thor's hauberk, a highly complex biological weave made of some kind of durable nanocarbon. In addition to its physical hardness, the armor indirectly protects Thor from ballistics, extreme heat and
  cold, cutting weapons, energy weapons, psychic attacks, vacuum, and it also protects against a few things that are hard to describe (due to Earth's primitive level of technology).
This is why Thor doesn't usually bother with a helmet, his armor is advanced enough that even his face is protect even though it's not covered. Anyways, the point is that the discs are the major component of his armor. Most of the rest of his armor (and a fair amount of Thor's combat toughness) is generated by the discs.
This is why Yasgardians prefer melee weapons.  Their defensive technology is so good that range is almost immaterial in combat. Bear in mind, Yasgardians are just sufficiently advanced aliens. Their technology may look like medieval armor and weaponry, but it only looks like that because Yasgardians like the aesthetics.
The primary example of this is Thor's hammer, a simple-looking weapon that can demolish buildings, call lightning, and exert enough force to pin a medium-angry Hulk to the floor.
Note: Most of this is speculation taken from SHIELD's data vault and compiled into the
  official report given to Congress on extraterrestrial threat assessment. The description is vague because Thor has to follow strict Yasgardian policies regarding civilizations which are less technologically-advanced. And even if he wanted to share his technology he would have a hard time explaining it because Thor is a  warrior, not an engineer.

If you believe them.
This talks about the mythology that the movie got wrong.
This talks about aspects of the movie and Thor's powers.
More fan talk.

A: In the Ultimate Universe, Thor's suit is called the European Defense Initiative Bio-Mechanical Suit.
You can read all about it at the above link, but basically, a team in Brussels was trying to create their own super soldier, using symbols from Norse mythology to create a suit that gave its wearer the ability to fly and super-strength.

One of the team members, Thorlief Golmen, had a mental breakdown and started to believe that he was Thor, the Norse god of Thunder. The team actually incorporated some of his ideas into the suit, adding things like weather control to its repertoire.
This answers your question: the circles were part of the suit, which gave its wearer Thor's powers.
Thorlief eventually escaped with the suit and became Thor. Loki, having infiltrated the team from Brussels, later convinced The Ultimates that Thor was just an escaped mental patient. They do manage to get the suit (the belt part of it) away from Thor, and he seemingly loses his powers, giving credence to the claim.
Perun, aka "Soviet Thor" at this point wears Thor's belt and circle-vest, which give him Thor's powers.

Thorlief then learns that he is indeed Thor, reborn in a human form. He then gets Thor's true powers and no longer requires the suit, or the circles.
Source: The Ultimates 2
And for more background on Ultimate Thor's use of his suit versus his god powers, wikipedia is always a good start.

A: The shiny circles on his shirt serve no clear purpose, even they are not a clear symbol like the Superman's "S" because there already a "T" symbol on Thor's belt.
The circles provide a nice disruption of the monotony and their shiny nature contrasts well with the black of Thor's tunic and the six circles are arranged in perfect symmetry and its served as the perfect look for an Asgardian God of Thunder.

A: There is little historical references in Marvel canon for the circles on Thor's chest tunic. He has had this costume since his first appearance in Journey into Mystery #83 (1952).

Can history be our guide?
With that said, we can look perhaps into history and see if we can determine what the artist Jack Kirby was hoping to show in this costume design. If we can assume this design was inspired by Thor being an ancient god of war, then perhaps it would be considered a stylized armor design. Thor being a superhuman being might have little use for armor in his day to day life, but might want to remind his enemies of his valor with a costume that could resemble an armor he may have worn at one time.

A closeup of the Lauersfort Phalera, Burg Linn Museum Center, Krefeld, Germany
One of the first and earliest potential armor designs which bears more than a passing resemblance would be the 120 AD, Legionary Roman armor. The phalerae medallions, the large disks share a similar placement (though not exact) on the Roman armor. The disk were usually covered with the faces of prominent leaders or mythical beasts denoting bravery or skill in battle.

From the Augustan period, both infantrymen and cavalry men received the same award when an opponent was killed and his equipment seized: a series of nine phalerae which gravestone reliefs show were worn on leather straps on the upper torso. Once again, these decorations were intended for soldiers up to the rank of centurions. --Armed Batavarians: Use and Significance of Weaponry and Horse Gear, by Johan Nicolay; Amsterdam University Press.

Turkish, Antique char-aina, (chainmail with mirror plates), Russian Zertsalo (Ottoman inspired)
The phalerae medallions were not unique to the Romans. The Celts wore similar devices for religious reasons and similarities could be found in ancient Mongolian, Chinese, Russian, Ottoman and Japanese armors, often designated mirror armors for their shiny appearance.
Art Imitates Life
Thor has had many different costume designs, many actually resembling armor rather than the cloth or leather of his early designs. These later designs were more inclined to use actual armor plates to depict the circles in his early costume designs, strengthening the appearance to phalerae medallions, even including ornate designs in some of them.

Conclusion
While we have no definitive proof the circles on Thor's early costume were indeed a representation of phalerae medallions, it is at least historically possible the original design may have been inspired by early armors from the Roman, Ottoman and Persian armor designs which incorporated similar elements.
Note: While Vikings did wear armor into battle, it has not been shown to be an integral part of the armor designs to wear phaelara into battle. Most vikings wore leather furs, cuirboilli (boiled hardened leather) or chainmail tunics with shields into battle.

A fairly realistic depiction of Viking armor and weapons circa the 5th century AD.


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Biografia
Nato a Dearborn e cresciuto a Canton (Michigan), si laurea all'Università del Michigan e continua i suoi studi artistici alla William Esper Studios di New York. Tra la fine degli anni novanta e l'inizio dei duemila intraprende la carriera di attore teatrale. Nel 2001 interpreta il ruolo del "Boy" nella prima statunitense Off-Broadway di The Play About the Baby vincendo un Clarence Derwent Award come più promettente interprete maschile. Debutta a Broadway nel 2003 nel revival Gypsy nella parte di Tulsa e interpreta Matt nel musical The Opposite of Sex, ruolo che riprende anche nel 2006.

Nel 2002 esordisce in televisione in un episodio della serie televisiva West Wing - Tutti gli uomini del Presidente e successivamente appare in Crossing Jordan, CSI: NY ed interpreta Scooter, l'ex fidanzato di Lily in How I Met Your Mother. Nel 2011 è nel cast del film A Very Harold & Kumar Christmas, terzo capitolo della serie di Harold & Kumar. Nel 2009 si diploma in arte culinaria al Le Cordon Bleu College di Pasadena realizzando il suo desiderio di diventare uno chef. Attualmente lavora come chef privato a New York e gestisce una compagnia di catering a Los Angeles. Nel 2014 affianca Jessica Lange, interpretandone il marito, nel finale di stagione della serie antologica American Horror Story: Freak Show, di Ryan Murphy. Nel 2015 è tornato a recitare a Broadway dopo una lunga assenza col il musical It Shoulda Been You, diretto da David Hyde Pierce e interpretato da Tyne Daly e Sierra Boggess.

Vita privata
Burtka dopo aver avuto una relazione di alcuni anni con il produttore Lane Janger, è legato dall'aprile 2004 al collega Neil Patrick Harris. Proprio la relazione con Burtka è stata la causa del coming out di Harris che nel novembre 2006, sei mesi dopo l'apparizione di Burtka in How I Met Your Mother, ha dichiarato alla rivista People di essere gay, anche per mettere a tacere le voci che lo accusavano di nepotismo e che sostenevano che Burtka avesse ricevuto la parte solo perché sentimentalmente legato alla star della serie.

I due attori sono apparsi per la prima volta in pubblico insieme come coppia alla cerimonia degli Emmy Award del 2007, mentre la prima volta insieme sul palco è del febbraio 2008 ad un evento di beneficenza della comunità LGBT di New York dove si sono esibiti nel duetto Take me or leave me del musical Rent. Il 12 ottobre 2010 sono diventati genitori di due gemelli, Harper Grace e Gideon Scott, nati da madre surrogata. Si sono sposati in Italia il 7 settembre 2014.

Filmografia

Cinema
24 Nights, regia di Kieran Turner (1999)
Harold & Kumar - Un Natale da ricordare (A Very Harold & Kumar Christmas), regia di Todd Strauss-Schulson (2011)
Annie and the Gipsy, regia di Russell Brown (2012)
Dance-off: Sfida a ritmo di danza (Platinum the Dance Movie), regia di Alex Di Marco (2014)
Cicada, regia di Matthew Fifer e Kieran Mulcare (2020)

Televisione
West Wing - Tutti gli uomini del Presidente (The West Wing) – serie TV, episodio 3x20 (2002)
Crossing Jordan – serie TV, episodio 5x06 (2005)
How I Met Your Mother – serie TV, 7 episodi (2006-2014)
Worldly Possession, regia di Adam B. Stein – film TV (2007)
CSI: NY – serie TV, episodio 4x05 (2007)
Neil's Puppet Dreams - serie TV, 7 episodi (2012-2013)
American Horror Story - serie TV, episodio 4x13 (2014)
Una serie di sfortunati eventi - serie TV, episodi 2x9, 2x10 (2018)
Blacker - serie TV, episodio 1x01 (2018)
Home Movie: The Princess Bride - miniserie TV, episodio 1x05 (2020)
Uncoupled - serie TV, 1x06 (2022)

Doppiatori italiani
Nelle versioni in italiano dei suoi lavori, David Burtka è stato doppiato da:
Felice Invernici in How I Met Your Mother (prima voce)
Luca Sandri in How I Met Your Mother (seconda voce)
Maurizio Fiorentini in Una serie di sfortunati eventi
Maurizio Merluzzo in Harold & Kumar - Un Natale da ricordare
Federico Di Pofi in Uncoupled

Note

Altri progetti

Collegamenti esterni

Persone che hanno fatto coming out
Cantanti da musical

redpajama_set_name: RedPajamaWikipedia


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It's part of an agreement between Eyellusion, which develops hologram technology, and Primary Wave Publishing, which owns the namesake and rights to some of Gould's music.
Organizers say details on performance dates will be announced in late 2019.
"Holographic" live performances have become a growing niche of the music industry as entertainment companies look to draw audiences with deceased performers. But usually the images are not technically 3D holograms.
At the 2012 Coachella music festival rapper Tupac Shakur, who was killed 15 years earlier in a shooting, appeared in what was often called a hologram. Technically, it was a two-dimensional image projected through mirrors and a screen.
HologramUSA is another company that's been showcasing its technology at live events. Earlier this year it delivered a montage of famous faces, both past and present, in a showcase at Toronto's Yonge and Dundas Square which featured Frank Sinatra, Jackie Wilson and members of the Black Eyed Peas.


Adelaide City hopes to solidify first place when it hosts West Adelaide in Round 22 of PlayStation 4 NPL South Australia at Adelaide City Park.
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Para Hills Knights and Adelaide Olympic battle it out at The Paddocks at 3:00pm for the sixth place anf Final Series Football.
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City only requires one point to finish out the season on top of the table. Damian Mori's side had the opportunity to seal first place last week, but succumbed to Adelaide Comets 2-1 at SA Athletics Stadium.
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The bass guitar is a fundamental part of pop and rock music. It propels the music and sits underneath the guitar and vocals, backing up the harmony, creating build, intensity and dynamic as well marking out the rhythm. It's easy to play simple bass but the mastery of rhythm is a sufficient challenge to last for years. The bass and drums together form the rhythm section. They are the engine room that drives the music forwards. Unlike good guitar players, who are a dime a dozen, good bass players are always in demand and are often the unsung hero of the band. Whenever a song makes you want to dance, you can guarantee there's a great bass line kicking in. The modern electric bass guitar developed from the double bass, and other traditional bass instruments. As techniques have evolved, the electric bass has come to be used as a soloing instrument in jazz, fusion, Latin, and funk styles, andbass solos can also be performed in other genres.
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Some time ago, 2015, someone in the PJRC forum asked me if it was possible to emulate the C64's SID chip on the Teensy 3.2. Since I had already had experience with the porting of audio codecs (mp3/aac/flac), I came up with the idea to search for a "finished" emulator and found the very good reSID. This is also used by VICE. The porting wasn't that difficult, but I've optimized some parts of it to better match the Teensy and its audio library. It is even possible to emulate a second reSID for stereo operation. Unfortunately, current reSID versions require a lot of RAM, so I had to switch to an older version - which is not necessarily worse. Soon the wish for a SID-Player came up and a little later the Teensy 3.6 was announced. With 256KB RAM, more than enough flash, SD slot and 180 MHz it seemed possible to emulate a complete C64. But before that, other hurdles had to be overcome. There was no way to control a display fast enough. However, the T3.6 has a fast SPI interface, which can be supplied via a DMA channel. The first display that crossed my mind was the well-known ILI9341, which had already done a good job for the T3.2. Some time before, a user in the forum had noticed that you can overclock its SPi interface drastically. After some attempts I had a working video player - even before the official release of Teensy 3.6. Paul Stoffregen thankfully provided me with an early pre-release version. After many preliminary considerations and deviations I came to the conclusion that the T3.6 should be capable of a C64 emulation. Unfortunately I forgot almost everything about the C64, and I had to and still have to learn everything anew and read a lot of technical details. I must admit that I have underestimated the VIC (the video chip of the C64) enormously. But that was a good thing, otherwise I would never have started this project. In the meantime I have rewritten the code for the VIC four times.
Load "whatever. prg" - Loads the program from the Teensy SD card.
Save "whatever. prg" - Saves the program.
Other commands such as "open" are currently NOT supported for Device 1. Disk-Containers like "D64" are not supported by this simple patch.
Access is ALWAYS made to a subdirectory "/C64/", which must be present on the SD card.
Thanks to Bill Greiman for his SdFat library with long file names. The C64 was able to support file names of 16 characters length in the 80's when Microsoft only supported 8+3 characters.
There are many more TODOs I would like to tackle little by little. The emulated VIC does not yet support the BA signal, and the emulated 6150 processor does not yet know it; -) Therefore there are some inaccuracies in the processor cycles. For example, the VIC can pause the processor or allow write access only. The latter has not yet been implemented. There's still work to be done on the internal timing of the sprites - so "Democoder"tricks like sprite stretching don't work. Also "xFLI" and "DMA Delay" is not yet possible. All things that the developers of the C64 didn't foresee at that time but were discovered by "hackers". Furthermore, only the PAL mode works satisfactorily - but this is only because I haven't found an NTSC program yet!
This project is "Open Source" and everyone is invited to work on it.
The board is exactly the size of the display.
Defragster, thank you very much for your help.
This boards uses one transitor and three resistors as bi-directional levelshifter - per line. It is not very fast (about 1.2uS on falling edge) , but fast enough for the C64. It needs a bit more power (mA) than the single 1k-resistors which Commodore used in ther devices. I read somewhere, that, normally, you can attach 8 devices to the bus. With this board, I wouldn't use more than 5-6.
Included is a file named "defs.h" that will do all the hard work you - if you replace the platform.txt of Arduino (latest 1.39) with the one which is attached to this post. It will not influence your other sketches.
Last edited by Frank B; 09-19-2018 at 06:15 PM.
Please help me with this list !
Others are not tested so far.
Last edited by Frank B; 11-05-2017 at 08:50 PM.
In the "extras" folder is a C64 Memorymap.
Just add this as last line to your setup() and see what happens..
- want real retro-feeling ? In vic-palette.h you can select a black&white palette, or settings for a green-display. You can choose other palettes, too, or create your own.
Last edited by Frank B; 10-31-2017 at 06:26 PM.
Use a good, clean soldering iron with not too much Watt (power) - 30 Watt are ok. Don't solder longer than a few seconds per soldering joint - if you need too, let it cool down and try again.
Solder the lowest/smallest parts first. First, the backlight-resistor, then the other 15 resistors. After that, the audio-connector and USB - then the pinheaders (Don't forget the USB-Host pins for the Teensy), transitors and the capacitor.
You'll need a small side cutter to shorten the female pinheaders - make sure not to cut too much by mistake! Don't worry if you loose one pin - that's normal.
Last step: solder the big Joystick-connectors and the IEC connector.
Double/tripple check if everything is ok, remove tin solder rests and clean the board. If you have a magnifying glass, please check that there are no unintended shorts or cold joints.
Last edited by Frank B; 09-27-2017 at 07:34 PM.
And you can soon get one Kurt, work with Frank PCB's and most parts to build 10 of them on there way to me - and I'll place a DigiKey order tomorrow to complete the kits for US addresses.
Easy to assemble and it works!
Frank - Re post #1 - also need F_CPU=240 MHz since the IDE defaults to 180 and that fails the F_BUS at 120 MHz.
Thanks I've added this, and a short "How to compile".
Does it make sense to add compiled hex-files to the repro (would mean some additional work for me with every update) ? Or is it easy enough to compile ?
It compiled easily enough for me with your DEFS installer. But if you made a Version_HEX for each update you would be able to try prior versions if an anomaly came up? And if somebody can't get it to build & Run they would have a known good hex if the hardware is built and soldered right.
Your solder directions look good. I saw a video recently where masking tape was used to keep the part in place. I got a bottle of 90% Isopropyl Alcohol and had good results with that. A clean old toothbrush to wet and wipe the area - rather than pouring on too much. Then I SAFELY get the board somewhat warm (from a distance at first) with a hair dryer to make sure there are no trapped pockets of liquid and quickly evaporate off any excess. Look for it to be clean and inspect. Of course I had one bad joint on USB - a nice shiny blob that was only on the pin and not mated to the PCB - DOH - worse was it worked on some devices so I assumed it was a software issue when it wasn't.
Added improved keyboard-scan. This fixes some problems with games that scan the keyboard-matrix with swapped in/outputs (i.e. "PAC-MAN").
"Bruce Lee" starts now - shows the "demo" perfectly- but crashes when start... hm - there must be an other reason I guess I need help with this game - any c64 specialists here ?
Last edited by Frank B; 09-11-2017 at 09:55 PM.
Last edited by Frank B; 10-08-2017 at 11:49 AM.
This looks great! Is there a link I can click on to order the kit?
RalphW - Send a PM to Frank for details. I just got a set of PCB's in the US - going to assemble one tonight with the parts kits complete to mail to those interested in the working ILI9341 version. Will take pics of the parts and as I have it assembled to upload soon.
I have a working VGA version on a breadboard - not with USB-HOST (flicker problems), but PS2 Keyboard connector.
Looks great on a big screen. VGA-Refresh is 60Hz, emulated PAL is 50Hz - so, due to these different frequencies, in some situations may be a bit flickering visible (have not seen this so far).
Still some work to do - the small TFT has no visible left/right borders, so they are not yet implemented for VGA. Then, new boards are needed - will take some time. I'll make a special price for those who ordered the TFT Version so far.
The board will be useful for other VGA-Projects (or as T3.6 board with some 5V leveshifts), too.
GitHub update for PS/2 & VGA follows in the next days.
Good news: A user reported that loading programs from a original disk drive works.
Last edited by Frank B; 09-27-2017 at 07:46 PM.
I am slowly making progress in compiling C64 but I am now stuck. using 1.8.4 and 1.39 I getting error "getname" no member in patches.cpp.
Hm. You're right, I havn't seen it in your logs. Can you try to remove the std SD-lib ?
Well, this shouldn't be needed as it works for me, but the problem is definately a confusion with these libs.
Unfortunately, the audio-lib wants SD.h and it is not easy to override this wihout editing the audio-lib or writing an own - I don't want this..
This is the reason, i add a "SD.h" file to the teensy64 library - this seems not to work for you.
@Defragster: You compiled it - did you have the same problem ?
I've decided to lower the price for the kit. The new price is 29 USD or 25 EUR.
Last edited by Frank B; 10-01-2017 at 02:27 PM.
I am now down to "ctags pattern are missing" issue. I have the same error now on windows 7 and ubuntu 15.10 64 bit machine.


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AUSTIN, Texas--(BUSINESS WIRE)--Mar 19, 2019--ATX Seed Ventures today announced the renaming of its firm to ATX Venture Partners with continued focus on early-stage venture capital investments in Texas and the broader South-Central U.S. technology landscape.
ATX Venture Partners is led by Shonk along with Partners and Co-Founders Brad Bentz and Danielle Allen. The news today comes on the heels of the firm's announcement of the close of its second fund for new high-growth technology companies and follow-on investments for current portfolio companies. The firm's focus is to bring institutional-grade funding, process and rigor to early-stage venture capital investments.
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Automatic segmentation of coronary angiograms based on fuzzy inferring and probabilistic tracking
Zhou Shoujun1,
Yang Jian2,
Wang Yongtian2 &
Chen Wufan1
Segmentation of the coronary angiogram is important in computer-assisted artery motion analysis or reconstruction of 3D vascular structures from a single-plan or biplane angiographic system. Developing fully automated and accurate vessel segmentation algorithms is highly challenging, especially when extracting vascular structures with large variations in image intensities and noise, as well as with variable cross-sections or vascular lesions.
This paper presents a novel tracking method for automatic segmentation of the coronary artery tree in X-ray angiographic images, based on probabilistic vessel tracking and fuzzy structure pattern inferring. The method is composed of two main steps: preprocessing and tracking. In preprocessing, multiscale Gabor filtering and Hessian matrix analysis were used to enhance and extract vessel features from the original angiographic image, leading to a vessel feature map as well as a vessel direction map. In tracking, a seed point was first automatically detected by analyzing the vessel feature map. Subsequently, two operators [e.g., a probabilistic tracking operator (PTO) and a vessel structure pattern detector (SPD)] worked together based on the detected seed point to extract vessel segments or branches one at a time. The local structure pattern was inferred by a multi-feature based fuzzy inferring function employed in the SPD. The identified structure pattern, such as crossing or bifurcation, was used to control the tracking process, for example, to keep tracking the current segment or start tracking a new one, depending on the detected pattern.
By appropriate integration of these advanced preprocessing and tracking steps, our tracking algorithm is able to extract both vessel axis lines and edge points, as well as measure the arterial diameters in various complicated cases. For example, it can walk across gaps along the longitudinal vessel direction, manage varying vessel curvatures, and adapt to varying vessel widths in situations with arterial stenoses and aneurysms.
Our algorithm performs well in terms of robustness, automation, adaptability, and applicability. In particular, the successful development of two novel operators, namely, PTO and SPD, ensures the performance of our algorithm in vessel tracking.
Accurate extraction of the coronary artery tree from coronary angiograms is important for the diagnoses, treatment, and clinical study of various coronary artery diseases. In particular, computer-assisted analysis can improve the performance of quantitative evaluation. It can reduce the inter- and intra-observer variations in determining the severity of coronary artery stenosis [1]. An efficient vessel extraction algorithm also enables the detection of coronary artery motion, as well as the reconstruction of 3D vascular structures from a single-plan or biplane angiographic system [2].
Anatomical structures, such as blood vessels, nerves, and bronchi, present themselves as line-liked structures in 2D images or as tubular structures in 3D images. Over the past 10 years, a variety of approaches have been developed for vessel segmentation from 2D and 3D medical images [3], which typically differ in terms of basic strategies or imaging modalities. Common segmentation approaches employ multiscale filters, morphological segmentations, deformable models, front propagation methods, tracking-based methods, and ridge traversal-based methods. Although many of these approaches are promising for vessel segmentation, developing fully automated, faster, robust, and accurate vessel segmentation algorithms remains highly challenging because of the complexity of vascular structures as well as large variations in image intensities and noise.
Tracking-based methods [4–9] exhibit a natural advantage in extracting arterial axis lines in the angiographic images because of their relative simplicity, as well as their adaptability to variations in vessel diameters. In addition, their ability to capture detailed quantitative descriptions of vessel axes, diameters, and boundaries, leads to high levels of accuracy. Traditional tracking-based methods, however, are guided by simple local features that limit their utility because of difficulties in efficiently integrating advanced features into canonical expressions for guiding the tracking. Therefore, the use of minimum cost functions or multi-scale filters [10–13] to construct the tracking operator poses several advantages in the segmentation of coronary angiograms; this approach, however, may also be problematic when meeting bifurcations or vessel crossings because it can follow only the path with the strongest response.
In this work, we propose a fully automatic tracking-based method that can adapt to varying vessel curvatures and diameters resulting from arterial stenoses or aneurysms. It can also walk across intensity gaps along the longitudinal vessel direction, and manage vessel bifurcations and crossings.
An integrated framework was designed to solve the challenging problem of coronary angiogram segmentation. The main components in this framework are summarized in Figure 1. The automatically detected seed point is generally located near the root of the arterial tree or on the main trunk. The probabilistic tracking operator (PTO) was initialized with the initial seed point to search for a candidate artery element with the most similar vessel geometries (including vessel feature, direction, and diameter) in the neighborhood. The vessel structure pattern detector (SPD) was utilized in parallel to classify each detected artery element as bifurcation or crossing. The artery element classified as bifurcation is placed on the list of source data to enable tracking new vessel segments beginning from this artery element in subsequent tracking. The tracking algorithm stops when all points on the list of source data are tracked.
Overview of the proposed tracking framework for the segmentation of X-ray angiograms with (a) Preprocessing step, (b) Tracking step, and (c) Results.
During the process mentioned above, local features and measures, such as the Gabor response, vessel path, skeleton-line, and directional consistency, were also analyzed to integrate the relational vessel attributes for probabilistic vessel tracking and structure pattern identification. The PTO is designed to incorporate local features and measures to determine candidate artery elements along the same vessel segment. These candidates were selected particularly from the overlapping region between the binarized vessel regions and a sampling disk centered at the current artery element under consideration. The size of the sampling disk corresponds to the current vessel diameter, thus rendering the PTO adaptive to varying vessel diameters in case of arterial stenoses or aneurysms. Simultaneously, the SPD works to infer the vessel structure pattern, such as the distal end, segment, bifurcation, and crossing. To complete structure pattern identification, the vessel feature profile scanned from a circle around the current artery element was analyzed and a fuzzy inferring function was applied. In particular, multiple features such as vessel feature, direction continuity, and Gabor responses at the peaks of the vessel feature profile were integrated into the fuzzy inferring function for pattern identification.
Vessel feature and direction maps
The intensity profile across the longitudinal direction of the vessel may highlight an elevation or even a slight intensity dip at the center, depending on the contrast between vessels and background. On the other hand, the profile along the longitudinal direction of the vessel can be smooth [Figure 2(b)]. Accordingly, the multiscale detection or enhancement of vessel structures can be completed by convolving angiographic image I(x) [where x = (x, y)] with normalized second-order Gaussian derivatives G (x; σ f ) at different scales σ f . The use of a Gaussian filter is important in reducing the influence of noise, properly shaping the line profile and ensuring a large second derivative across the vessel.
Show the angiographic images, feature maps and the cross-sectional profiles of coronary artery. (a1) and (a2) depict two original angiographic images; (a3) and (a4) are their vessel feature maps, respectively. Subfigure (b) depicts the cross-sectional profiles of the vessel in the original image and in the corresponding feature map.
In 2D cases, let ∇2 I (x, σ f ) be a Hessian matrix combined with Gaussian convolution for angiographic image I(x). It can be written as
∇ 2 I ( x , σ f ) = − σ f 2 ⋅ { ( ∂ 2 ∂ x ∂ x ∂ 2 ∂ x ∂ y ∂ 2 ∂ y ∂ x ∂ 2 ∂ y ∂ y ) G ( x , σ f ) } ∗ I ( x )
where G (x; σ f ) denotes a Gaussian filter with standard deviation σ f .
The bright line structure on a dark background can be reflected by a Hessian matrix with a large negative eigenvalue λ1 and a small eigenvalue λ2 of positive or negative sign; that is λ1 < 0 and |λ2| ≪ |λ1|. Various response functions have been proposed in previous studies [11–13]. We provide a similar response function to extract the vessel structures by thresholding the eigenvalue map using a low threshold |r λ |, expressed in
Z ( x , σ f ) = { ln ( | λ 1 ( x , σ f ) | ) + c λ 1 < r λ 0 else
where c is a constant. Note that λ1 is negative in our case, with r λ = − 2 π σ f . This response equation provides a vessel discriminant function at scale σ f . To integrate multiscale responses corresponding to different scales at each location x, we select the maximum response across multiple scales, i.e.
Z ∧ ( x ) = max ( Z ( x ; σ f ) ) , σ f = σ 1 , ... , σ n
where σ1 and σ n are the minimum and maximum scales, determined according to the range of vessel diameters in the angiographic images. In this paper, 14 scales were used. For convenience, the resulting vessel features are normalized to 0[1] in this paper. Vessel feature map Z ∧ ( x ) (Figure 2 (a3-a4)) may also be binarized for extracting the vessels, and may further be thinned to obtain the skeletal lines representing the vessels.
The vessel direction map is estimated using the best detected scale. First, the maximum of absolute eigenvalue |λ1| is obtained at each location x by | λ o p t ( x ) | = max σ f | λ 1 ( x ; σ f ) | . Assuming that the eigenvector corresponds to λ opt (x) is v opt (x), the direction orthogonal to v opt (x) is then selected as the vessel direction at x. For convenience, we again use v 2 to represent the estimated vessel direction map later in this paper.
Therefore, using this step of multiscale analysis, we obtain three separate maps from the original angiographic images, namely, a vessel feature map, a vessel direction map, and a map of skeleton lines. Next, an initial seed point x 0 is automatically detected from a point within the thinned vessel skeleton-lines, as well as with maximum vessel feature intensity Z ∧ ( x 0 ) . The determined initial seed point is generally located near the root of the arterial tree or the main trunk of the arterial tree. The data above are used for the identification of consequential vessel pattern.
Probabilistic tracking of coronary artery
A dynamic mechanism was designed for our tracking framework. First, a list for source points (called source-list) was maintained to keep the initial seed point, as well as the vessel bifurcations that were detected during the vessel tracking procedure. In addition, a second list of crossings (called crossing-list) was designed to keep the possible crossings of two vessels. Then, a sampling disk with about half the size of the vessel diameter was used in the PTO to automatically track the artery segments (or branches) one at a time, beginning from the seed point and stopping at the vessel termination. During the tracking, the proposed SPD functioned simultaneously to report the local vessel pattern as bifurcation, crossing, segment, or termination. All detected vessel bifurcations were stored one at a time at the top of the source-list and were later used as subsequent starting points for tracking their respective artery segments (or branches). Finally, the vessel PTO and the SPD stop tracking and identifying vessels once all vessels have been tracked and registered.
Tracking criterion
The tracking mechanism was designed based on the criterion of continuity properties of luminance, position, and diameter of the general coronary artery in the angiographic images. The appropriate incorporation of these properties into the PTO enables successful management of the cases of vessel gap (caused by nonuniformity of the contrast medium or inappropriate thresholding in the preprocessing step) and arterial lesion (such as stenosis or aneurysm).
Description of PTO
Our PTO performs automatically along the coarse vessel path extracted from the vessel feature map. It begins or stops tracking an artery segment (or branch), depending on the structure pattern detected at current artery element e t . The tracking problem at simple artery positions, with no bifurcations, crossings, or terminations, is to determine the next artery element e t+1in the vessel path. Each artery element e t has four associated attributes, namely position x t , vessel feature Z ∧ ( x t ) , direction vector ϕ t = v 2(x t ), and vessel diameter d t . These attributes guide the vessel tracking algorithm. For efficiency, a sampling disk centered at the current artery element e t was used to search for a set of candidate elements { ( x t + 1 i , Z ∧ ( x t + 1 i ) , ϕ t + 1 i , d t + 1 i ) | i ∈ [ 1 , ... , N s ] } from the overlapping region between the sampling disk and the binarized vessel feature map. From artery element t to t+1, the probabilistic tracking can be formulated by a maximum posterior probability (MAP), expressed as
x ∧ t + 1 = arg max i ∈ [ 1 , ... , N t ] P ( x t + 1 i | x t )
The sequent modeling was based on the aforementioned continuity properties of the artery vessel. During tracking vessel length [Figure 3(a)], three local terms were used to constrain the candidates based on vessel feature continuity, longitudinal direction continuity, and diameter continuity. The first term, Z ∧ ( x t + 1 i ) , was acquired from the vessel feature map at candidate position x t + 1 i . The second term to some extent, kept the vessel tracking from being interrupted by noise, pseudo contours, and crossing, although more assurances should come from the structure pattern detection result, as described in aforementioned sections. Given vector V t + 1 i pointing from current position x t to candidate point x t + 1 i , a deflection of vessel direction θ t + 1 i = ∠ V t + 1 i − ∠ ϕ t [Figure 3(a)] yields a means of the longitudinal continuity. In the case of vessel crossing or paralleling with each other (especially for thin vessels), the third term of diameter continuity enables the tracking of the current vessel segment/branch to proceed without being affected by neighboring vessels. Given d t + 1 i and d t as the vessel diameters, respectively at candidate point x t + 1 i and current artery element x t , increment ∇ d t + 1 i = | d t + 1 i − d t | yields the measure of diameter continuity. Altogether, the estimation of the optimal candidate gives emphasis to the continuity properties, which is also the basic idea for probabilistic tracking. In the following paragraph, we provide further discussion to mathematically model.
Show the probabilistic tracking and diameter measurement along vessel path. (a) is the description of the probabilistic tracking. (b) depicts the estimation of vessel diameter using the vessel feature profile of transversal line C t + 1 i .
First, the relationship between the sampling instance and the posterior probability can be described as
( Z ∧ ( x t + 1 i ) ; θ t + 1 i ; ∇ d t + 1 i ) | x t → P ( x t + 1 i | x t )
All feature measures in the left of the abovementioned expression are normalized before participation in the estimation of probability. In particular, maximal vessel feature Z ∧ max and maximal diameter d max are determined from all N s candidate points in the sampling disk, and are used to normalize the respective measures. Note that in practice, estimated vessel direction ∠ϕ t can be reversed; thus, it should be considered in the normalization of θ t + 1 i . Given normalized measures Q Z ( x t + 1 i ) = | 1 − Z ∧ ( x t + 1 i ) / Z ∧ max | , Q θ ( v t + 1 i ) = 1 π min { | arg θ t + 1 i − π | , | arg θ t + 1 i | } , and Q d ( x t + 1 i ) = ∇ d t + 1 i / d max , their probabilities can be respectively written as:
q Z ( x t + 1 i ) = 1 2 π σ Z , t ⋅ exp ( − Q Z 2 ( x t + 1 i ) 2 σ Z , t 2 )
q θ ( x t + 1 i ) = 1 2 π σ θ , t ⋅ exp ( − Q θ 2 ( x t + 1 i ) 2 σ θ , t 2 )
q d ( x t + 1 i ) = 1 2 π σ d , t ⋅ exp ( − Q d 2 ( x t + 1 i ) 2 σ d , t 2 )
where σ Z,t , σ θ,t , and σ d,t are the standard deviations, which can be estimated by calculating the variances of the corresponding measures in all N s candidates. For example, σ Z,t is estimated as
σ Z , t = 1 N s ∑ i = 1 N S [ Q Z ( x t + 1 i ) − Q ¯ Z ] 2
where Q ¯ Z is the average measure obtained by Q ¯ Z = 1 / N s ∑ i = 1 N s Q Z ( x t + 1 i ) . By integrating all distribution functions in Eq. (6), the optimal estimation of artery element e t+1can be obtained by
e t + 1 = x ∧ t + 1 = arg max x t + 1 i , i = 1 , ... , N s ( q z ( x t + 1 i ) ⋅ q θ ( x t + 1 i ) ⋅ q d ( x t + 1 i ) )
PTO uses adaptive parameters adjusted according to Eq. (7) based on all candidates in the sampling disk. Thus, it can successfully estimate the artery elements along the vessel path even in cases of gaps and arterial lesions. The gap is generally regarded as the region of a longitudinal narrow crack with a width less than the vessel radius, whereas the arterial lesion presents as a short or long component of the longitudinal region with large variations in vessel diameter and, at times, weak luminance. During the vessel tracking, the candidates running into the gaps can be crossed out by the continuity terms, thus enabling PTO to continue working. On the other hand, in case candidates run into the regions of the artery lesion, the PTO still carries on, even with large variations in vessel diameter.
Artery diameter estimation
Considering that the blood vessels have measurable abnormalities in diameter, intensity, and tortuosity, the artery diameter of candidate x t + 1 i should be estimated adaptively by analyzing its 1-D vessel feature profile orthogonal to the vessel direction. All candidates sitting along the sample profile have the same vessel diameter estimated (as described next). For example, in Figure 3(b), another candidate x t + 1 j sitting at the peak of the profile has the same vessel diameter as x t + 1 i . The profile can be represented by transversal line C t + 1 i with a single pixel width, as shown in Figure 3(b). Candidates x t + 1 i and x t + 1 j have the same profile, and thus the same diameter.
The feature values in the particular profile can be obtained from vessel feature map Z ∧ . The vessel diameter on this profile can be measured through the convolution of the normalized second derivative of the 1-D Gaussian function with the profile. Standard deviation σ in the 1-D Gaussian function should be adjusted during the vessel diameter estimation. Standard deviation σ ∧ that results in the largest response among all convolution results with the use of different standard deviations is finally selected as the estimated diameter for all candidates sitting on the same profile. Using this method, we can estimate vessel diameter d t + 1 i for candidate x t + 1 i .
This vessel diameter estimation process proceeds automatically without user interaction. The relevant diameter estimation results are demonstrated in the experimental section.
Inferring structure pattern of artery vessel
When the PTO works on current artery element x t , the SPD should also work in parallel to report the structure pattern to guide the PTO. Our SPD performs in the following manner. First, a circular pattern detector is centered on current artery element x t . It then acquires the circular cross-section profile from vessel feature map Z ∧ . Subsequently, it captures local vessel measures, including the number of peaks in profile (M t ), the azimuth vector directing from the detector center to every peak (p m ), and the Gabor response on each peak (γ o.m ). Finally, it returns the structure pattern inferred by a fuzzy inferring operator using the fuzzy membership degrees of multi-feature fuzzy subsets.
Detecting the peaks of the vessel-feature profile
The pattern detector samples of vessel features Z ∧ along the circular cross-section profile are centered at current artery element x t with radius r t = α·d t /2. Generally, the range of parameter α in α ∈ [1,1.5] is preferred for better measurement because in this case, the radius of circular pattern detector is a little bit larger than half of vessel diameter d t of current artery element x t ; thus, the structure around x t can be adaptively and completely captured. The resulting vessel feature profile is called circular template T (x,r,t), which consists of a fixed number (e.g., 150) of vessel features sampled over the circumference of a circle (x t , r t ). The same number of vessel features Z ∧ is sampled to make the SPD adaptive to different sizes of vessel diameters. Therefore, even for small vessels, the same number of points is also sampled. Because vessel feature map Z ∧ is defined in discrete domain, the bilinear interpolation is used for sampling features from Z ∧ when generating circular template T (x,r,t).
The sampling process is demonstrated in Figure 4, in which the vessel feature profiles are sampled by the circular templates (T (x,r,t)) in 4(a2)-4(c2). The typical profiles are shown in 4(a3) - 4(c3). To detect the peaks in each profile, first-order derivative dT (x,r,t)of T (x,r,t)is computed through the circular convolution of T (x,r,t)with the first-order derivative of the 1-D Gaussian filter. Figures 4(a4) - 4(c4) shows the magnitude profile of the resulting first-order derivative |dT (x,r,t)|. The local minima of the derivative magnitude correspond to the maxima or minima of the vessel feature profile along T (x,r,t). The peaks of the profile corresponding to maxima can be detected according to the derivative signs. For example, a peak of the profile corresponds to the sign transition of the first-order derivative from positive to negative. In this manner, we can detect all peaks along with their locations [e.g., z{p m = (x m , y m ), m = 1,...,M t }], where M t is the total number of peaks.
Using the circular pattern detector to characterize the vessel structures, in the cases with bifurcation, paralleling, and crossing patterns. (a1)-(c1) are original images and the respective regions of interest. (a2)-(c2) are the corresponding direction maps overlaping with circular pattern detectors. (a3)-(c3) are the corresponding vessel-feature profiles on the circular template T (x,r,t). (a4)-(c4) are the corresponding magnitude profiles of the first-order derivative dT (x ,r,t).
The resulting peaks provide the SPD vessel with several important properties, such as their positions, vessel features, vessel directions, as well as their relationships with the center of pattern detector (x t ). To better infer the pattern of the vessel structure, more relevant metric features, such as the Gabor features described in the next section, should be extracted.
The Gabor responses at locations of the peaks
Considering that the peaks of the circular profile provide useful information for structure identification, we first discuss how to infer the case in which two points (apart less than a few pixels) are located at the same vessel axis line. This case may also be called "co-vessel." To detect whether peak point p m = (x m , y m ) and detector center (O d ) are located in the same segment of the vessel, the Gabor filter operator [14, 15] was used for local description. As a function of orientation, frequency, and scale, the operator can characterize the dominant attributes at peak point p m = (x m , y m ). Note that this responds strongly to the isolated vessel strip, but exhibits a weaker or no response to the noise.
Given the relationship between the Gabor filter scale and the frequency with 2σ = 2πf = T, several masks by the Gabor operator can be defined by the real component of the Gabor function with a size of T × T. The masks of different scales are shown in Figure 5(b). Thus, to characterize local attributes, such as direction and "co-vessel" at a peak point, we merely need to compute the responses of several Gabor masks, and retain only the related parameters corresponding to the maximum response. Although none of these parameters are invariant to common image transformation, such as scaling and rotation, only one set of parameters corresponds to maximum response g max at the considered position. Given vector V o,m directing from the detector center to the peak position (x m , y m ), the following response measure γ o,m represents the degree with which peak p m = (x m , y m ) belongs to the same vessel axis line of the center point of the pattern detector
The feature integration, Gabor masks, and structure detection near artery bifurcation. (a) illustrates circular pattern detector and feature integration. (b) is an examples of five Gabor masks, and their parameters, where (b1) T 1 = 5, θ 1 = π/2, f 1 = 0.2; (b2) T 2 = 9, θ 2 = π/2, f 2 = 0.111; (b3) T 3 = 13, θ 3 = π/2, f 3 = 0.077; (b4) T 4 = 9, θ 4 = 3π/4, f 4 = 0.111; (b5) T 5 = 5, θ 5 = 3π/4, f 5 = 0.2. (c) illustrates the problem of the uncertainty of the node positions.
γ o , m = 1 g max arg max σ | G ∠ V o , m , σ / π , σ ( x m , y m ) |
Where 0 < γ o.m < 1. With an image sized 512 × 512, the size of the mask (σ) is equal to the vessel diameter, which ranges from 3 to 14 pixels. Therefore, the resulting measure γ o,m reflects the relationship between peak p m and the detector center. For example, the resulting measure γ o,m at peak p m is lower if mask orientation V o,m does not accord with the local vessel direction, that is, there is no "co-vessel" existing between the peak point and the detector center.
The multi-feature based fuzzy inferring function (FIF)
Four types of patterns can be inferred, namely, vessel termination (i = 1), artery segment (i = 2), bifurcation (i = 3), and crossing point (i = 4), where variable i denotes the index for the ordinal structure pattern of the artery vessel. With effects from noise and pseudo edge, the number of peaks in each of these four types of patterns might be higher than the actual one. For example, by comparing the circular cross-section profile of different cases (Figure 4), we can observe that more than two peaks might occur in the profile of the artery segment, and more than three or four peaks might occur in the profile of the bifurcations or crossings, respectively. Without loss of generality, the circular pattern detector detects the number of peaks from the ordinal structure pattern according to M t ≥ 1, M t ≥ 2, M t ≥ 3 and M t ≥ 4 [Figure 5(a)]. Thus, the number M t can be regarded as a pseudo pattern of the artery structure. On the other hand, each peak p m has two metric features important to pattern identification: vessel feature Z ∧ ( p m ) at peak p m , and response measure γ o,m of Gabor mask function G ∠ V o , m , σ / π , σ ( x m , y m ) . The relationship between the pattern detector and the metric features for a typical artery bifurcation is shown in Figure 5(a).
In the following section, the fuzzy subsets are defined for all metric features, as well as for number of peaks M t . They will then be integrated for pattern inferring of point x t .
Definition 1: In the region Ω = { p m , Z ∧ m , γ o , m , M t | 1 ≤ m ≤ M t ; Z ∧ m , γ o , m ∈ [ 0 , 1 ] } , given that fuzzy subsets F m , Z ∧ and F m,γ correspond to the metric features of peak p m , and fuzzy subset F M t , x t i corresponds to the i-th pseudo pattern at current position x t , the membership degrees of these fuzzy subsets can be defined by the standard Gaussian function as
μ m , Z ∧ = exp ( ( Z ∧ max − Z ∧ m ) 2 − 2 σ Z 2 ) ; μ m , γ = exp ( ( γ max − γ o , m ) 2 − 2 σ γ 2 ) ; μ M t , x t i = { exp ( ( M t − i ) 2 − 2 σ M t 2 ) M t ≥ i 0 else
where. Z ∧ max = max m Z ∧ m ., γ max = max m γ o,m , and m = 1,...,M t . The above expressions, μ m , Z ∧ and μ m,γ , represent the respective degrees of membership of two metric features at current position x t , which are used to ensure that each peak p m is located at the center of the vessel. Meanwhile, μ M t , x t i provides the membership degree of the pseudo pattern based on the number of peaks. According to the abovementioned membership degrees, the structure patterns of current position x t can be inferred by the following definition.
Definition 2: In the same region Ω, given J i (x t ) the fuzzy subset of the structure pattern belonging to the i-th pattern at current position x t , the relationship between fuzzy set J i (x t ) and the fuzzy sets of the metric features is given by
J i ( x t ) = { I m = 1 M t F m , Z ∧ } I { I m = 1 M t F m , γ } I { F M t , x t i }
The membership degree of J i (x t ) is given by:
μ J i ( x t ) = ( ∧ m = 1 M t μ m , Z ∧ ) ∧ ( ∧ m = 1 M t μ m , γ ) ∧ μ M t , x t i
where it is shown that the direct inferring of the local vessel structure can be hardly implemented using μ J i ( x t ) > T α with threshold T α . Therefore, the optimal pattern inference should be based on the principle of maximum membership degree and can be expressed as
μ J i 0 ( x t ) = ∨ i = 1 4 [ μ J i ( x t ) ]
which infers the artery structure at current position x t belonging to the i 0-th pattern.
When the detector center is near the vessel node (e.g., bifurcation or crossing), the resulting node position can be ambiguous; for example, a few of the redundant positions may possibly be the node positions because of the similarity of their metric features to those of the actual node. To solve this problem, a second local maximum operation is performed to obtain a preferable node position. Given n redundant positions near the bifurcation, with the membership degrees { μ J i 3 ( x t 1 ) , ... , and μ J i 3 ( x t n ) } , the preferable one should be located at
x ∧ = arg max x t k , k = 1 , ... , n ( μ J i 3 ( x t k ) )
In Figure 5(c), the numbers 2 and 3 represent the two structure patterns determined in the corresponding locations by the proposed pattern detector. Pattern detection result is used to guide the vessel tracking process.
Manipulation of vessel tracking process and organiztion of tracking results
Appropriate termination conditions for vessel tracking are important to achieving better tracking performance. Our vessel tracking algorithm stops tracking the current artery segment or branch once one of the following conditions is satisfied: (1) a new vessel bifurcation is detected, which should be dealt with appropriately; (2) vessel feature Z ∧ ( x t + 1 ) at position x t+1along the vessel path is below a certain threshold, such as when a value is slightly higher than the background (this threshold is set as 0.05 in this paper); (3) the current path overlaps with a vessel path previously detected, except when a crossing point on the vessels has been detected and recorded in advance; (4) the source-list is empty and no new node is found; and (5) the new point is outside the image field. In all cases except for vessel crossing, the last valid vessel point is marked as a termination point, and the algorithm starts tracking the other vessel with the seed point placed at the top of the source-list.
The artery segment is a vessel length with two end-points at two nodes, or at an origin point and a node, whereas the artery branch is a distal vessel with a distal point. Either the artery segment or branch is composed of artery elements. Considering these artery elements arranged at intervals (or with "look-ahead distance") of less than the radius of the sampling disk, polylines are used to connect the artery elements by linear interpolation. The generated polylines are treated as an approximation of vessel centerlines, and have high probability inside the binarized vessel structures.
The proposed algorithm was tested on both simulated images and real image sequences with stenosis vessel and aneurysm. To obtain images with acceptable quality, the cranial and caudal angles, as well as the X-ray dose, were adjusted so that the X-rays travel a moderate distance. Our vessel tracking algorithm was implemented in MATLAB 7.0 on a Pentium IV PC (with CPU 2.8 G and 512 M memory).
Our algorithm was first tested on various simulated artery vessel images to adjust its parameters. Actual images were used to evaluate the actual performance of the algorithm by comparing the algorithm-segmented structure and vessel length of the entire artery network with those produced by expert cardiologists. The tracking algorithm has several distinguishing characteristics: (a) it is robust to the starting position detected; (b) it can detect and identify a larger area of the artery tree without any manual intervention; and (c) it can accurately distinguish the narrows resulting from the gaps in the vessel feature map or those caused by real vessel stenosis.
In our algorithm, total computational time T consisting of two major components T 1, T 2, and one minor component T 3, were spent on preprocessing (36.7 s), tracking (15.7 s), and connecting artery elements (1.4 s), respectively.
General effects of vessel segmentation are listed in the first column of Table 1, where the results of right coronary artery (RCA) and the left coronary artery (LCA) in the real angiographic images are compared separately. In Table 1, L ∑ and L ¯ denote the length of algorithm-segmented vessels (in pixels) and the total vessel length delineated by expert cardiologists, respectively. The percentage of the detected artery segments (DAS %) and the extracted vessel length (EVL %), as well as the identification ratio (IR %) of the arterial structure was computed to evaluate the performance of our algorithm. In particular, the IR % is defined as the percentage of the correct parts of vessel length in the entire length of algorithm-segmented vessels. As openly reported in literature, the DAS % produced by Haris et al. [16] reached 90%, while the EVL % produced by Schrijver et al. [4] was less than 78%. On average, our algorithm can reach 94.7% for DAS % and 88.1% for EVL %.
Table 1 Statistical results on artery tracking and structure identification in real angiographic images.
Other detailed experiments and performances are introduced in the next section.
Arterial vessel simulation and algorithm evaluation
Simulated data were created for the arterial segment [Figure 6(b)] and the simulated arterial tree (SAT) [Figure 6(c)]. In particular, various levels of Gaussian smoothing were applied to simulate the spatial blurring in an X-ray projection. The SAT in Figure 6(c) was generated to simulate artery characteristics, such as curving, overlapping, and bifurcating. For these simulated images, all information related to vessel segments, centerline, and local structure are known beforehand. We can analyze the algorithm characteristics given that various levels of white Gaussian are added to these images.
The simulations of arterial vessels: (a) the local coordinate system of vessel simulation; (b) the simulated arterial segments; (c) the SAT.
The performance of our algorithm can first be evaluated using the simulated images, such as vessel segments A to F. Given an initial seed point at the left end of the vessel segment in A, B, E, and F of Figure 6(b), the PTO can automatically track vessels and measure their diameters. The measured diameters along the vessel are consistent with varying morphology, such as stenoses and aneurysms. The resulting mean errors are listed in Table 2, where L x denotes the length of the simulated arterial segment, e 0 and e d denote the mean error of the resulting vessel centerlines and diameters, respectively. Under zero-level Gaussian noise, the mean errors of estimated centerlines and diameters of stenosis or aneurysm vessels are no more than 0.02 and 0.04, respectively. In case of close proximity (such as C) and local gap (such as D), the tracking results depend on distance d P between two neighboring vessels and gap-width w G , respectively. Suppose that r 1 and r 2, and r D denote the radii of two neighboring vessels and the radius of the detector, respectively. To enable the algorithm to operate through the vessel despite influence from the neighboring vessel and the gaps, the limiting distance and gap-width would be d P ≥ (r 1 + r 2)/2 and w G < r D , respectively. The entire length of the skeleton lines of the SAT is 948 pixels, and is entirely involved in the testing.
Table 2 Parameters and mean errors in testing of the phantoms of arterial segments.
The results of structure identification on the SAT and real angiograms are provided in the following sections.
Experiments on structure pattern inferring
Two experiments were performed on simulated and real images to test the capability of our algorithm to infer the structure patterns in the artery tree. The performances on identification of all four different patterns, as well as separate performances on the detection of bifurcation are reported.
The first experiment was conducted on the SAT image. Based on results of estimated membership degrees μ J i ( X t ) in Eqs. (13) and (14), the attributes of all interesting points in Figure 6(c) can be well characterized by our algorithm. Overall, the captured membership degrees corresponded well to four different structure patterns, such as the membership degree distribution between N1-N4 in Figure 7. For vessel overlapping cases, such as local superposition between the two vessel segments N2-N4 - N5-D and N1-N4-N5-C, the structure ambiguity (between N4 and N5) might be difficult to resolve using only a single-view projection, although it might be resolved by observing vessel motion or radius information from sequence images as done by human observers while reading cine-angiograms. In short, our multi-feature based fuzzy inferring method is capable of accurately estimating the structure patterns from 2D images.
The fuzzy memberships measured along the vessel axis, starting from point N1 to N4 in the SAT.
The second experiment was performed on actual angiogram images selected from the angiogram sequences. The related results are provided in the second and third columns of Table 1. The lower level of the arterial structure can be inferred with higher IR %, and the recognizable vessels can reach up to the fifth level at best. In practice, the cardiovascular surgeon is often interested in the vessels below the fourth level; thus, the performance of our algorithm is promising. The second column of Table 1 also displays the rate of bifurcation identification (Nb/Wb). Here, Nb denotes the number of correctly detected bifurcations for the b-th level vessel branch, while Wb (≥Nb) denotes the total number of the detected bifurcations, including the incorrectly detected ones.
Experiments on vessel tracking and measurement
We also evaluated the respective contributions of the probability terms of the continuity properties given in Eq. (6) to the vessel tracking. By rewriting Eq. (8) as x ∧ t + 1 = f ( q θ , q Z , q d ) , three different types of PTO, namely, x ∧ t + 1 = f ( q θ ) , x ∧ t + 1 = f ( q θ , q Z ) , and x ∧ t + 1 = f ( q θ , q Z , q d ) , can be constructed. Their respective results are compared in Figure 8, where the paths traced in the same sub-image were obtained by the same PTO. Figures 8(b1) and 8(b2) show that the direction constraint term in Eq. (6.2) can effectively compel the sampling disk and the pattern detector to move ahead, but it can often be lost in edges, pseudo contours, neighboring vessels, or even noise. By incorporating the vessel feature term, that is, using x ∧ t + 1 = f ( q θ , q Z ) , the vessel tracking result can be improved, as shown in Figures 8(c1) and 8(c2). Using all terms together, that is, using x ∧ t + 1 = f ( q θ , q Z , q d ) , the vessel tracking result can be further improved; this is reflected as the smooth and accurate tracking paths detected in Figures 8(d1) and 8(d2). In addition, if only the vessel feature or diameter term is used, the tracking model almost stops near the initial seed position. These visual results are not shown here.
Comparison of the results of vessel-tracking using the PTO based on different continuity terms. (a1) & (a2) two original images. (b1) & (b2) using the PTO simply based on q θ . (c1) & (c2) using the PTO based on q θ and q z . (d1) & (d2), using the PTO based on complete terms. (e1) & (e2), measuring the vessel diameters, respectively along the vessel paths in (d1) and (d2).
Figures 8(c1) and 8(c2) also yield a typical case in which the algorithm can successfully manage the close proximity or crossing of vessels, as well as varying vessel curvatures, which validates a number of attractive characteristics of the PTO. For example, the algorithm can run across the local vessel gap, proceed along the current vessel branch in spite of crossing, and successfully manage arterial stenoses and aneurysms.
The diameter estimation errors at the artery elements are less than 0.23 pixels on average. The results of the axis line estimation along the artery segments in the SAT image indicate that more errors appear near the nodes, with 1.36 pixels on average. These results show that the axis line estimation error at the nodes is controlled within a limited extent. For actual angiograms, we compared the automatically extracted arterial axis lines with the standard arterial centerlines delineated by an expert cardiologist. We also obtained good results, with a mean error of 0.17 pixels and the maximum error close to half of the respective vessel radius. These errors are produced by noise, as well as large curvatures or abnormal morphologies at the locations of vessel nodes.
Vessel stenosis
We tested a simple method to determine the position and severity of coronary artery stenosis in the given images, which can be used as an additional evaluation criterion for our tracking algorithm. Our algorithm was able to detect the arterial stenosis. An example in which the diameter of arterial stenosis is tracked and measured is shown in Figure 9. According to stenosis evaluation using the grading scheme of the visual analysis of the American Heart Association [17], %-LENGTH stenosis is estimated as %-LENGTH stenosis = (1-L r /L m ) × 100%, where L r and L m are the estimates of the minimal diameter of the stenotic part of a vessel and the mean diameter of the nonstenotic part, respectively. During tracking and detection, the vessel length of interest begins or terminates when %-LENGTH is 25% higher or lower than the minimum classified value. The vessel length of interest can be described by the rectangular sash in Figure 9.
Tracking and measuring vessel width using the real angiographic images with arterial stenosis. (a) Original angiogram with arterial stenosises; (b) Location and measurement of the stenosises.
In the testing, 35 angiograms with 40 stenosis positions were used to evaluate the correctness of stenosis identification, in which all the standard vessel stenoses, as well as their severities were provided beforehand by the expert cardiologist. As a result, 33 stenosis objects are correctly detected and the number of false negatives and false positives are seven and one, respectively. The average correctness rate of stenosis severity identification reaches 68.3%, in comparison with the given stenosis severity levels.
In this paper, we analyzed image data and vessel structures within X-ray projections. A structure distinction exists between the crossing and bifurcation of vessel segments. Two crossing vessel segments have no spatial structure connection, whereas vessel bifurcations (which in general produce three vessel segments) have a structural connection among them. Vessel bifurcation enables low-level vessel segment separation to two high-level ones at the bifurcation point where these vessel segments have different features in their diameters and direction continuity. However, in single-view X-ray projection, two spatial overlapping vessel segments may appear connected to each other at a crossing-point, where the vessel segments maintain their respective features of diameter and direction continuity near the point. The abovementioned vessel continuity of different cases can address, in part, 2D structure ambiguity.
In our algorithm, three parameters can be adjusted to achieve better segmentation results. These include threshold value r λ in the vessel function Eq. (2), the radius of sampling disk r S , and the radius of pattern detector r D . These parameters can be adjusted according to the overall performance integrated from the three percentages, DAS %, EVL %, and IR %. For instance, parameter r λ may be optimized according to
lim r λ → r λ ' Δ D A S ( r λ ) + Δ E V L ( r λ ) + Δ I R ( r λ ) Δ r λ ⋅ ( D A S ( r λ ) + E V L ( r λ ) + I R ( r λ ) ) → 0
The optimization for parameters r S and r D can be conducted similarly. Using the simulated images with different levels of noise, we can determine the optimal values for these three parameters. In the absence of noise, r λ is computed as r λ = − 2 π σ f
; parameters r S and r D turn out to be equal, that is, r S = r D , and are both equal to current diameter d t of the vessel under tracking.
In the experiments, the time spent in tracking depends on the length of the detected vessel, look-ahead distance s t , and vessel diameter d t . Look-ahead distance s t is determined by the diameter of the sampling disk, which is designed to vary with the diameter of current vessel d t . The ranges of these parameters are 1 ≤ s t ≤ 7 (pixels) and 3 ≤ d t ≤ 15 (pixels), respectively, which agree with the required relationship 1 ≤ s t ≤ d t /2. Similarly, more artery elements can result in more computational time.
The rate of bifurcation identification (Nb/Wb) in the second column of Table 1 is related to EVL % and independent of IR % because the IR% is calculated only by the detected vessel points. In addition, the IR % of bifurcation and crossing are relatively lower than that of other structure patterns, which is mostly caused by the structure ambiguity in the 2D image acquisition. According to the testing on SAT, the error ratio is correlated with the effects of image noise and the diameter of the detector.
Based on the results on 40 stenosis objects, the application for the diagnosis of stenosis severity levels do not appear to be very reliable because of the use of single-view projection images. The accurate quantification and analysis of stenotic lesions is actually very complicated and has been elaborately discussed by Sato et al. in [18]. The importance of designing an acquisition system for acquiring "good" images, in which stenotic lesions can be displayed clearly, rather than simply analyzing the given images by common clinic systems, is therefore important.
We developed a vessel tracking framework for the segmentation and measurement of the arterial tree in angiographic images, and applied it to actual clinical data. Based on the various evaluation results using both simulated and actual data, our algorithm demonstrates a very impressive performance in tracking and measuring artery trees. The particular advantages include efficient handling of vessel nodes, such as bifurcation or crossing; distinguishing between bifurcations and crossings, and automatically locating their positions; and automatic adaptation to varying vessel diameters in the coronary artery. These advantages were made clear with the introduction of our tracking strategies.
Our algorithms are able to locate stenosis or aneurysm positions in a number of given images. Naturally, the actual 3D morphology cannot be simply inferred through the 2D structure patterns. The use of 2D angiograms can pose ambiguity in determining vessel connectivity, particularly in cases with vessel overlapping. This indicates the importance of extending our algorithm to 3D applications to achieve certain diagnostic functions. Moreover, although our fuzzy inferring function is found relatively effective in integrating spatial characteristics of centerline, orientation, diameter, and density along the coronary blood vessels, the performance of structure pattern identification might be further improved, if we can effectively employ advanced learning-based methods, such as support vector machine, to identify the vessel structure patterns. These ideas will be explored further in our future studies.
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This work was partly supported by the National Basic Research Program of China (Grant No. 2010CB732505) and the National Science Foundation of China (Project No. 60772120, and Project No. 60902103). We would like to thank the Cardiac Center of Beijing Chaoyang Hospital and the Radiology Department of Tianjin General Hospital for clinical assistance and providing coronary angiogram data.
School of Biomedical Engineering, Southern Medical University, Guangzhou, 510515, China
Zhou Shoujun & Chen Wufan
Department of Optic electronics engineering, Beijing institute of technology, Beijing, 100081, China
Yang Jian & Wang Yongtian
Zhou Shoujun
Wang Yongtian
Chen Wufan
Correspondence to Chen Wufan.
ZS carried out the studies on image pre-processing, modeling of vascular structure inferring and tracking, and drafting the manuscript. CW conceived of the study, and participated in its design and coordination, and helped in the drafting of the manuscript. YJ carried out the data acquisition and simulated the coronary artery tree. WY checked the paper writing. All authors read and approved the final manuscript.
Shoujun, Z., Jian, Y., Yongtian, W. et al. Automatic segmentation of coronary angiograms based on fuzzy inferring and probabilistic tracking. BioMed Eng OnLine 9, 40 (2010). https://doi.org/10.1186/1475-925X-9-40
Vessel Diameter
Membership Degree
Artery Segment
Vessel Segment

redpajama_set_name: RedPajamaCommonCrawl


An ATM machine which was stolen in the early hours of yesterday morning, Tuesday, April 16, has been recovered by police.
The machine was taken from a premises in the Market Square area of Bushmills using a stolen digger, tractor and low loader.
The Antrim theft was the ninth such robbery to take place in Northern Ireland this year, with each incident causing devastation on local communities, according to the Police Service of Northern Ireland (PSNI).
I understand the fear that these attacks are causing, and the damage that is left in the wake of each theft. We are doing all we can to catch the people responsible and stop these attacks.
The constable noted that machinery owners are taking on board advice to secure and lock up equipment and install immobilisers, which have helped to prevent theft.
"I want to appeal to anyone who has any information about today's ATM theft in Bushmills to speak to us. Did you see a digger on a low loader being towed by a tractor on the roads in the area? Did you witness the attack just before 3.30am [yesterday] morning?
A telehandler was also used in the commission of this crime and I believe this was used to transport the ATM from the Diamond area of Bushmills.
The inspector added that the PSNI would like to talk to anyone who saw or heard anything in the area of the Ballyhome Road at the time.


text:
Maui to Impose New Hotel Tax due to Influx of Tourists
© Engin Yapici - Unsplash
Hawaii's lawmakers are rushing to allow counties to collect a three per cent tax from visitors staying at hotels and other short-term rentals.
Reasons for change
Before the new law, Hawaii had a ten per cent hotel tax rate, and the state then distributed tax revenue to five counties Maui, Honolulu, Hawaii, Kalawao and Kauai.
However, Oahu in Honolulu typically receives most of the funds due to its population size, even though Maui attracts more tourists per capita. The new law allows Hawaii's counties to collect a three per cent tax from visitors staying at any short-term rentals and keep the revenue for local needs.
The push for more revenue
As tourism has exploded in Maui, causing Maui's mayor Michael Victorino to beg airlines for visitor pause, officials on Maui are moving quickly to implement the new tax on tourists. "This will help tremendously," Maui council chair Alice Lee said, "Instead of $23 million, we'll probably receive in the neighbourhood of $50 to $70 million." Now counties will receive revenue based on the number of visitors and Maui stands to benefit most from the new law.
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