Datasets:
Dataset Viewer
image
imagewidth (px) 3
1.29k
| latex
stringlengths 3
4.96k
| latex_norm
stringlengths 5
5.62k
| page_id
stringlengths 15
15
| expr_type
stringclasses 2
values |
|---|---|---|---|---|
$S(\phi )$ | $ S ( \phi ) $ | 0001015_page002 | embedded |
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$\phi $ | $ \phi $ | 0001015_page002 | embedded |
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$\exp (-Ht)$ | $ e x p ( - H t ) $ | 0001015_page002 | embedded |
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$\psi (x)$ | $ \psi ( x ) $ | 0001015_page002 | embedded |
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$d\mu $ | $ d \mu $ | 0001015_page002 | embedded |
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$x$ | $ x $ | 0001015_page002 | embedded |
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$x(t)$ | $ x ( t ) $ | 0001015_page002 | embedded |
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$V$ | $ V $ | 0001015_page002 | embedded |
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$H= L +V(x)$ | $ H = L + V ( x ) $ | 0001015_page002 | embedded |
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$L$ | $ L $ | 0001015_page002 | embedded |
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$x(t)$ | $ x ( t ) $ | 0001015_page002 | embedded |
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\begin {equation} H = \half p^2 + V(x) \end {equation} | \begin{equation*} H = \frac { 1 } { 2 } p ^ { 2 } + V ( x ) \end{equation*} | 0001015_page002 | isolated |
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\begin {equation}\label {EVeq} \exp (-Ht) \psi (x) = \int d\mu \exp \left ( -\int _0^t V((x(s)) ds \right ) \psi (x(t)) \end {equation} | \begin{equation*} \operatorname { e x p } ( - H t ) \psi ( x ) = \int d \mu \operatorname { e x p } ( - \int _ { 0 } ^ { t } V ( ( x ( s ) ) d s ) \psi ( x ( t ) ) \end{equation*} | 0001015_page002 | isolated |
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$x: I \to M$ | $ x : I \rightarrow M $ | 0001015_page003 | embedded |
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$I$ | $ I $ | 0001015_page003 | embedded |
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$[0,t]$ | $ [ 0 , t ] $ | 0001015_page003 | embedded |
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$M$ | $ M $ | 0001015_page003 | embedded |
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$n$ | $ n $ | 0001015_page003 | embedded |
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$g$ | $ g $ | 0001015_page003 | embedded |
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$\omega =dh$ | $ \omega = d h $ | 0001015_page003 | embedded |
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$M$ | $ M $ | 0001015_page003 | embedded |
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$\omega = \Omu (x) d\Xmu $ | $ \omega = \omega _ { \mu } ( x ) d x ^ { \mu } $ | 0001015_page003 | embedded |
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$\omega = \Omu (x) d\Xmu $ | $ \omega = \omega _ { \mu } ( x ) d x ^ { \mu } $ | 0001015_page003 | embedded |
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$\dot {x}^{\mu }(t')= \frac {d{x}^{\mu }}{d t'}$ | $ \dot { x } ^ { \mu } ( t ^ { \prime } ) = \frac { d x ^ { \mu } } { d t ^ { \prime } } $ | 0001015_page003 | embedded |
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$S[x(.)] = i(h(x(t))-h(x(0)))$ | $ S [ x ( . ) ] = i ( h ( x ( t ) ) - h ( x ( 0 ) ) ) $ | 0001015_page003 | embedded |
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$x(t)$ | $ x ( t ) $ | 0001015_page003 | embedded |
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$\omega =0$ | $ \omega = 0 $ | 0001015_page003 | embedded |
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$h$ | $ h $ | 0001015_page003 | embedded |
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$M$ | $ M $ | 0001015_page003 | embedded |
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$\omega =dh$ | $ \omega = d h $ | 0001015_page003 | embedded |
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$\Pmu $ | $ p _ { \mu } $ | 0001015_page003 | embedded |
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$\Xmu $ | $ x ^ { \mu } $ | 0001015_page003 | embedded |
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$n$ | $ n $ | 0001015_page003 | embedded |
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$H(p,x)= \Pmu \Xmu - \Lag (x,\dot {x})$ | $ H ( p , x ) = p _ { \mu } x ^ { \mu } - L ( x , \dot { x } ) $ | 0001015_page003 | embedded |
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$H(p,x)= \Pmu \Xmu - \Lag (x,\dot {x})$ | $ H ( p , x ) = p _ { \mu } x ^ { \mu } - L ( x , \dot { x } ) $ | 0001015_page003 | embedded |
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$\omega $ | $ \omega $ | 0001015_page003 | embedded |
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$\Pb {\Tmu }{T_{\nu }}=0$ | $ \{ T _ { \mu } , T _ { \nu } \} = 0 $ | 0001015_page003 | embedded |
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$\Pb {\Tmu }{H_c}=0$ | $ \{ T _ { \mu } , H _ { c } \} = 0 $ | 0001015_page003 | embedded |
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$\Tmu $ | $ T _ { \mu } $ | 0001015_page003 | embedded |
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$\psi (x)$ | $ \psi ( x ) $ | 0001015_page003 | embedded |
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$\Pmu =-i \Dmu $ | $ p _ { \mu } = - i \partial _ { \mu } $ | 0001015_page003 | embedded |
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$\Pmu $ | $ p _ { \mu } $ | 0001015_page003 | embedded |
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$-i\DDmu $ | $ - i \nabla _ { \mu } $ | 0001015_page003 | embedded |
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$\XXmu \psi =0$ | $ X ^ { \mu } \psi = 0 $ | 0001015_page003 | embedded |
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$\XXmu =g^{\mu \nu } (p_{\nu } + i\omega _{\nu })$ | $ X ^ { \mu } = g ^ { \mu \nu } ( p _ { \nu } + i \omega _ { \nu } ) $ | 0001015_page003 | embedded |
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\begin {equation}\label {ACeq} S[x(.)] = \Intot i\Omu (x(t'))\dot {x}^{\mu }(t') \, dt' \end {equation} | \begin{equation*} S [ x ( . ) ] = \int _ { 0 } ^ { t } i \omega _ { \mu } ( x ( t ^ { \prime } ) ) \dot { x } ^ { \mu } ( t ^ { \prime } ) \, d t ^ { \prime } \end{equation*} | 0001015_page003 | isolated |
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\begin {equation}\label {MOMeq} \Pmu = \frac {\delta \Lag }{\delta \dot {x}^\mu } = i\Omu , \end {equation} | \begin{equation*} p _ { \mu } = \frac { \delta L } { \delta \dot { x } ^ { \mu } } = i \omega _ { \mu } , \end{equation*} | 0001015_page003 | isolated |
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\begin {equation} \Tmu \equiv \Pmu - i\Omu . \end {equation} | \begin{equation*} T _ { \mu } \equiv p _ { \mu } - i \omega _ { \mu } . \end{equation*} | 0001015_page003 | isolated |
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\begin {equation}\label {GTeq} \delta _{\epsilon }\psi (x) =-i \epsilon (\Dmu \psi (x) + \Omu (x) \psi (x)) \end {equation} | \begin{equation*} \delta _ { \epsilon } \psi ( x ) = - i \epsilon ( \partial _ { \mu } \psi ( x ) + \omega _ { \mu } ( x ) \psi ( x ) ) \end{equation*} | 0001015_page003 | isolated |
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$\Etamu $ | $ \eta ^ { \mu } $ | 0001015_page004 | embedded |
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$\Pimu $ | $ \pi _ { \mu } $ | 0001015_page004 | embedded |
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$(2n,2n)$ | $ ( 2 n , 2 n ) $ | 0001015_page004 | embedded |
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$\Etamu ,\Pimu $ | $ \eta ^ { \mu } , \pi _ { \mu } $ | 0001015_page004 | embedded |
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$\nabla $ | $ \nabla $ | 0001015_page004 | embedded |
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$\psi (x,\eta )$ | $ \psi ( x , \eta ) $ | 0001015_page004 | embedded |
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$\Pmu =-i \DDmu $ | $ p _ { \mu } = - i \nabla _ { \mu } $ | 0001015_page004 | embedded |
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$\Pimu = -i\frac {\partial }{\partial \Etamu }$ | $ \pi _ { \mu } = - i \frac { \partial } { \partial \eta ^ { \mu } } $ | 0001015_page004 | embedded |
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$\psi (x,\eta )$ | $ \psi ( x , \eta ) $ | 0001015_page004 | embedded |
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$(n,n)$ | $ ( n , n ) $ | 0001015_page004 | embedded |
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$SM$ | $ S M $ | 0001015_page004 | embedded |
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$\Xmu ,\Etamu $ | $ x ^ { \mu } , \eta ^ { \mu } $ | 0001015_page004 | embedded |
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$Q$ | $ Q $ | 0001015_page004 | embedded |
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$Q=\Etamu \Tmu =-i\Etamu (\Dmu + \omega )$ | $ Q = \eta ^ { \mu } T _ { \mu } = - i \eta ^ { \mu } ( \partial _ { \mu } + \omega ) $ | 0001015_page004 | embedded |
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$Q=\Etamu \Tmu =-i\Etamu (\Dmu + \omega )$ | $ Q = \eta ^ { \mu } T _ { \mu } = - i \eta ^ { \mu } ( \partial _ { \mu } + \omega ) $ | 0001015_page004 | embedded |
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$\chi $ | $ \chi $ | 0001015_page004 | embedded |
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$\chi = \Pimu \XXmu = -ig^{\mu \nu } \Pimu (\nabla _{\nu }-\omega _{\nu })$ | $ \chi = \pi _ { \mu } X ^ { \mu } = - i g ^ { \mu \nu } \pi _ { \mu } ( \nabla _ { \nu } - \omega _ { \nu } ) $ | 0001015_page004 | embedded |
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$M$ | $ M $ | 0001015_page004 | embedded |
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$\psi (x,\eta )$ | $ \psi ( x , \eta ) $ | 0001015_page004 | embedded |
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$Q=-i\Emh d \Eph $ | $ Q = - i e ^ { - h } d e ^ { h } $ | 0001015_page004 | embedded |
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$\chi = \Eph \delta \Emh $ | $ \chi = e ^ { h } \delta e ^ { - h } $ | 0001015_page004 | embedded |
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$d$ | $ d $ | 0001015_page004 | embedded |
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$\delta = *d*$ | $ \delta = \ast d \ast $ | 0001015_page004 | embedded |
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$h$ | $ h $ | 0001015_page004 | embedded |
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$\chi =\Pimu \XXmu $ | $ \chi = \pi _ { \mu } X ^ { \mu } $ | 0001015_page004 | embedded |
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$h$ | $ h $ | 0001015_page004 | embedded |
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$Q$ | $ Q $ | 0001015_page004 | embedded |
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$h$ | $ h $ | 0001015_page004 | embedded |
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$H_g$ | $ H _ { g } $ | 0001015_page004 | embedded |
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\begin {equation}\label {SPBeq} d\Pmu \wedge d \Xmu + \nabla \Pimu \wedge \nabla \Etamu + \frac 12 dx^{\mu } \wedge dx^{\nu } \Curv {\mu }{\nu }{\kappa }{\lambda }\eta ^{\kappa }\pi _{\lambda }, \end {equation} | \begin{equation*} d p _ { \mu } \wedge d x ^ { \mu } + \nabla \pi _ { \mu } \wedge \nabla \eta ^ { \mu } + \frac { 1 } { 2 } d x ^ { \mu } \wedge d x ^ { \nu } R _ { \mu \nu \kappa } { } ^ { \lambda } \eta ^ { \kappa } \pi _ { \lambda } , \end{equation*} | 0001015_page004 | isolated |
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\begin {eqnarray}\DDmu \psi (x,\eta ) = \Dmu \psi (x,\eta ) + \Gam {\mu }{\nu }{\lambda } \eta ^{\nu } \frac {\partial }{\partial \eta ^{\lambda }}\psi (x,\eta ). \end {eqnarray} | \begin{equation*} \nabla _ { \mu } \psi ( x , \eta ) = \partial _ { \mu } \psi ( x , \eta ) + \Gamma _ { \mu \nu } ^ { \lambda } \eta ^ { \nu } \frac { \partial } { \partial \eta ^ { \lambda } } \psi ( x , \eta ) . \end{equation*} | 0001015_page004 | isolated |
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\begin {eqnarray}H_g &=& i( Q \chi + \chi Q) \End &=& d \delta + \delta d + g^{\mu \nu }\Omu \omega _{\nu } -i (\Pimu \eta ^{\nu } - \eta ^{\nu }\Pimu ) \frac {\partial ^2 h }{\partial \Xmu \partial x_{\nu }}. \end {eqnarray} | \begin{align*} H _ { g } & = & i ( Q \chi + \chi Q ) \\ & = & d \delta + \delta d + g ^ { \mu \nu } \omega _ { \mu } \omega _ { \nu } - i ( \pi _ { \mu } \eta ^ { \nu } - \eta ^ { \nu } \pi _ { \mu } ) \frac { \partial ^ { 2 } h } { \partial x ^ { \mu } \partial x _ { \nu } } . \end{align*} | 0001015_page004 | isolated |
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$H_g$ | $ H _ { g } $ | 0001015_page005 | embedded |
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$x_t,\eta _t$ | $ x _ { t } , \eta _ { t } $ | 0001015_page005 | embedded |
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$SM$ | $ S M $ | 0001015_page005 | embedded |
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$\Xmu ,\Etamu $ | $ x ^ { \mu } , \eta ^ { \mu } $ | 0001015_page005 | embedded |
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$b_t$ | $ b _ { t } $ | 0001015_page005 | embedded |
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$(\theta _t,\rho _t)$ | $ ( \theta _ { t } , \rho _ { t } ) $ | 0001015_page005 | embedded |
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$(d+ \delta )^2$ | $ ( d + \delta ) ^ { 2 } $ | 0001015_page005 | embedded |
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$J$ | $ J $ | 0001015_page005 | embedded |
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$u:\Sigma \to M$ | $ u : \Sigma \rightarrow M $ | 0001015_page005 | embedded |
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$\Sigma $ | $ \Sigma $ | 0001015_page005 | embedded |
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$2m$ | $ 2 m $ | 0001015_page005 | embedded |
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$M$ | $ M $ | 0001015_page005 | embedded |
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$H^{\alpha }_{\mu }$ | $ H _ { \mu } ^ { \alpha } $ | 0001015_page005 | embedded |
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$\Etamu $ | $ \eta ^ { \mu } $ | 0001015_page005 | embedded |
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$\pi ^{\alpha }_{\mu }$ | $ \pi _ { \mu } ^ { \alpha } $ | 0001015_page005 | embedded |
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$\alpha =1,2$ | $ \alpha = 1 , 2 $ | 0001015_page005 | embedded |
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$\Sigma $ | $ \Sigma $ | 0001015_page005 | embedded |
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$\mu =1,\dots ,2 m$ | $ \mu = 1 , \ldots , 2 m $ | 0001015_page005 | embedded |
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$M$ | $ M $ | 0001015_page005 | embedded |
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in Data Studio
IBEM Cropped: Bounding Box Mathematical Expressions from Scientific Pages
A processed version of the IBEM Dataset (Anitei et al., 2023), designed for the training and evaluation of image-to-markup models, expression recognition, and related document understanding tasks. Each sample in this dataset consists of a cropped image region containing a single mathematical expression (either displayed or embedded), along with its corresponding LaTeX annotations.
Dataset Summary
This dataset is derived from the original IBEM dataset by extracting individual mathematical expressions using the provided bounding boxes, and cropping them from their original document pages. All page-level coordinates were specified as percentages and converted to absolute pixel coordinates during cropping.
Each record includes:
- A cropped image of the mathematical expression.
- The original LaTeX string (
latex). - A normalized LaTeX string (
latex_norm) with visual formatting removed. - The ID of the original page.
- The expression type (
isolatedorembedded).
Dataset Structure
Features:
features = Features({
"image": Image(),
"latex": Value("string"),
"latex_norm": Value("string"),
"page_id": Value("string"),
"expr_type": Value("string"),
})
Splits:
The dataset is split into standard train, val, and test subsets based on the official partition lists provided by the authors (Tr*.lst, Va*.lst, Ts*.lst).
Source
Citation:
Anitei, D., Sánchez, J. A., & Benedí, J. M. (2023). The IBEM Dataset: a large printed scientific image dataset for indexing and searching mathematical expressions (1.0) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.7963703
Original Dataset Description
The IBEM dataset consists of 600 LaTeX documents with a total of 8,272 pages, containing:
- 29,603 displayed mathematical expressions
- 137,089 embedded mathematical expressions
These were extracted from the LaTeX source files of documents in the KDD Cup Collection. The dataset supports a variety of tasks, including:
- Mathematical expression detection and extraction
- LaTeX recognition from printed page images
- Indexing and search of STEM content in large-scale document archives
Preprocessing Notes
- Preamble fields containing LaTeX macros were excluded.
- All expressions were cropped to their respective bounding boxes and stored as image snippets.
- Only the
latexandlatex_normfields were retained for expression text. - Expressions split across multiple lines were treated as-is, using the duplicated complete LaTeX string provided by the original dataset.
Licensing
Distributed under the same license as the original IBEM dataset. Creative Commons Attribution 4.0 International
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