Pith. sign in

REVIEW 4 major objections 6 minor 28 references

HishabNet: Detection, Localization and Calculation of Handwritten Bengali Mathematical Expressions

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A detector that reads handwritten Bengali math expressions end-to-end, reporting 98.6% mAP and solving 132 of 140 test expressions.

desk verdict A YOLOv3-based Bengali digit detector with a new bounding-box dataset, undermined by an internally inconsistent expression-grouping algorithm and evaluation that is too thin to support the strong claims. read the letter →

arxiv 1909.00823 v1 pith:W5BSNG7Z submitted 2019-09-02 cs.CV cs.LG

Md Nafee Al Islam , Siamul Karim Khan This is my paper · ORCID
classification cs.CVcs.LG
keywords BengalihandwrittendigitsobjectdetectionYOLOv3mathematicalexpressionrecognitionHishabdatasetCNNmathlocalization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that handwritten Bengali mathematical expressions can be recognized and evaluated by treating digits and operators as objects to detect, rather than as a single classification problem. The authors build a YOLOv3-based detector, train it on a new annotated dataset they call Hishab, and show that the detected boxes can be grouped into expressions and computed. They report a validation mAP of 98.6% and that the full system correctly solves 132 of 140 test images of varying complexity. If true, this would be a working pipeline for an under-served script and a step beyond single-digit classification.

What carries the argument

The central mechanism is YOLOv3, a one-stage object detector that predicts bounding boxes and class probabilities from a single convolutional pass. Detected objects are then assembled into expressions by Algorithm 1, which sorts detections by x-center and groups them by the vertical extent of the leftmost box, using a 0.5×height margin. This spatial grouping is what lets the system turn isolated digit detections into multi-digit numbers and expressions.

What would settle it

Feed the system a handwritten expression containing a fraction such as 3/4 or a superscript like $2^{3}$. If the grouping algorithm cannot reconstruct the expression (e.g., it merges numerator and denominator or misorders the superscript), then the horizontal-sorting assumption is invalid and the claimed end-to-end capability does not extend to these common notational forms.

Watch

Extended reading notes

Core claim

The paper's central claim is that a single-stage object detection network, YOLOv3 with a Darknet-53 backbone, can simultaneously localize and classify Bengali numerals and arithmetic operators in an image, and that those detections contain enough spatial information to reconstruct numbers and perform arithmetic. The authors introduce the Hishab dataset of 40,000 annotated images spanning 18 classes, report an overall validation mean average precision of 98.6%, and demonstrate correct evaluation of handwritten expressions in categories ranging from single-digit arithmetic to multi-digit decimal expressions with brackets and multiple expressions per image. They also report that the same backbone, when trained as a classifier, achieves 99.6252% accuracy on NumtaDB and 99.0833% on CMATERdb.

Load-bearing premise

The method assumes that a mathematical expression is always arranged horizontally, so that sorting detected objects by their horizontal centers and grouping by the leftmost object's vertical span is enough to reconstruct the expression; this breaks for fractions, superscripts, and vertically staggered layouts.

Editorial extensions

If this is right

  • If the reported performance holds, the same detection-plus-grouping approach could be applied to other under-resourced scripts, since the method does not depend on Bengali-specific features beyond the training data.
  • The Hishab dataset could support further research on Bengali handwritten object detection, as it is the first dataset of its kind with bounding-box annotations for digits and operators.
  • The system's ability to handle multiple expressions in one image suggests that document-level math recognition, not just isolated equations, is feasible with this architecture.
  • The reported classifier accuracies on NumtaDB and CMATERdb indicate that the backbone CNN is a competitive feature extractor for Bengali digit recognition.
  • The grouping heuristic, if extended to handle fractions and superscripts, could generalize the system to a wider class of mathematical notation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the expression-assembly step is the actual bottleneck: the detector itself is evaluated only on detection mAP, while the end-to-end accuracy (132/140) is a joint measure of detection and grouping, so failures could stem from either stage. A natural extension is to replace the hand-crafted grouping with a learned parser or a graph neural network over detected boxes.
  • The 0.5×height margin in Algorithm 1 is a free parameter that is not cross-validated. Its sensitivity could be tested by perturbing it on a held-out set, and such a test would quantify how robust the grouping is to variations in handwriting size and spacing.
  • The same architecture could be evaluated on handwritten math in other scripts, or on printed math, to see whether the detection-driven approach transfers without re-engineering the grouping logic.
  • Because the dataset is synthetic in part (augmentations applied to a primary dataset), the reported mAP may be optimistic relative to fully natural handwritten images; a test on a separate real-world dataset would clarify this.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes HishabNet, an end-to-end system that uses YOLOv3 to detect and localize handwritten Bengali digits, operators, brackets, decimal points, and equals signs, and then forms and evaluates arithmetic expressions by grouping detections according to their positions. The model is trained on a newly created "Hishab" detection dataset of 40,000 images, reports a validation mean average precision of 98.6%, and achieves 132/140 correct calculations on a custom test set of expression images; the backbone is also evaluated on the NumtaDB and CMATERdb classification benchmarks.

Significance. The core idea is sensible and the paper makes a concrete, falsifiable claim: a YOLOv3 detector plus simple positional grouping can evaluate handwritten Bengali arithmetic. If the result holds, it is a useful engineering demonstration, and the Hishab dataset with bounding-box annotations could be a resource for the community. Credit is due for reporting quantitative results on a new dataset and for testing the backbone on public benchmarks; nevertheless, the paper's own evidence is currently too thin: the grouping algorithm is not reproducible as written, the expression-evaluation protocol is undefined, and no baseline comparisons or external validation are provided.

major comments (4)
  1. [Section III-D, Algorithm 1] The pseudocode is internally inconsistent, so the claimed end-to-end calculation cannot be reproduced from the text. If column 2 is the x-center, as implied by the instruction "Sort I according to xcenter, I_{i;j=2}", then Ymin/Ymax are computed from x-centers and the membership test compares only the height (column 4) against that span, never checking vertical position; if column 2 is instead the y-center, the preceding sort is not by x. The paper provides no code, no corrected pseudocode, and no runnable specification, and this algorithm is the sole mechanism for converting detections into expressions. Please supply a corrected, unambiguous algorithm and either a reference implementation or a worked example showing how the test-set images are grouped.
  2. [Section IV, Table III] The "correct prediction" criterion is undefined, and the failure analysis is missing. It is not stated whether a correct image requires the final numeric answer only, or also perfect detection, grouping, and parse order; the eight failures, including four in the hardest "multiple expressions" category, are not analyzed, so the reader cannot tell whether errors come from the detector, the grouping heuristic, the calculator, or the test-set construction. Specify the evaluation metric and report per-stage error counts and examples of failure, especially for the 16/20 multiple-expression category.
  3. [Section III-D, grouping heuristic] The algorithm assumes expressions are horizontally arranged and uses the vertical span of the leftmost box plus a hand-chosen 0.5-times-height margin. This is stated as sufficient for identifying and evaluating multiple mathematical expressions, but fractions, superscripts, subscripts, and vertically staggered terms are not represented in Table III, even though they are common in handwritten mathematics. The claim should be restricted to single-line horizontal expressions until these cases are shown to work, or the test set and algorithm should be extended to cover them.
  4. [Sections I and IV, validation] The validation is not yet sufficient to support the performance claims. The 98.6% mAP is computed on the authors' own validation split, with no stated IoU threshold, no class-wise AP, and no comparison to any other detector; Table II is a reproduction of published results for other algorithms on COCO and is not an evaluation of this model. Likewise, the abstract's "outperforms previously suggested architectures" is not supported by any head-to-head comparison in the results. I recommend adding a baseline comparison on Hishab, reporting class-wise AP and the IoU criterion, and, if the claim is to be made, benchmarking the backbone against published methods on the same public splits.
minor comments (6)
  1. [Section III-B, dataset description] The arithmetic is slightly inconsistent: 18 classes with nearly 2,180 images per class plus 800 multi-class images gives about 40,040 images, not 40,000, and the construction of the 800 multi-class images and the annotation format should be described precisely.
  2. [Section II-E, Table I] The classification of a wrong-class box with IoU above the threshold as FN is nonstandard; most detection evaluations would count a correctly localized but misclassified box as a false positive, so please justify or correct the convention.
  3. [Section III-A, Equation (2)] Equation (2) has a typographical issue with the leading label and the superscript/subscript placement, and the notation "IOU truth pred" is hard to read; please re-typeset and renumber the equations consistently.
  4. [Section IV, mAP reporting] The paper never states the IoU threshold t used for the mAP calculation, nor whether mAP is averaged over the 18 classes equally; without this information the 98.6% figure is not reproducible.
  5. [Section IV, test set] The 140-image expression test set is described only as containing expressions of "various complexities"; please state how it was constructed, whether it is a subset of the Hishab validation split, and whether it is disjoint from the training data.
  6. [General, reproducibility] The Hishab dataset, trained weights, and evaluation scripts are not made available, and no repository URL is given; a public release would be necessary for the results to be independently verified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all claimed results are empirical evaluations (standard YOLOv3 training, a new detection dataset, and external backbone benchmarks), and no derivation reduces to its own inputs.

full rationale

The paper makes no formal derivation whose output equals an input by construction. The object detector is the standard YOLOv3 pipeline trained and evaluated on a held-out validation split of the authors' own Hishab dataset; the k-means anchor-box fitting on training data is standard practice and does not force the reported mAP, which is measured on validation images not used for fitting. The backbone CNN is tested on two public datasets, NumtaDB and CMATERdb, providing external, non-circular evidence. The expression-grouping heuristic in Algorithm 1 is underspecified and internally inconsistent as printed, which is a reproducibility and correctness risk, not circular reasoning, because the claimed 132/140 end-to-end correctness is an empirical outcome that is not assumed in defining the inputs. No load-bearing self-citation, imported uniqueness theorem, or renamed known result appears; the only self-referential element is that the headline mAP is computed on the authors' own dataset, which weakens external validation but does not make the result equivalent to its inputs.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim depends on the correctness of YOLOv3, on the reliability of the newly created Hishab dataset (which is not public), and on a very simple heuristic for grouping digits into numbers and expressions. No new physical or model entities are introduced. The two free parameters are the k-means anchor boxes and the hand-chosen grouping margin in Algorithm 1.

free parameters (2)
  • anchor boxes = (14,17), (23,31), (34,56), (68,70), (42,118), (117,111), (105,185), (170,151), (219,218)
    Anchor box dimensions are fit via k-means clustering on the training set (Section III-A). This is standard for YOLOv3 but is a dataset-specific choice that affects detection performance.
  • Expression grouping margin coefficient = 0.5 (box height of the leftmost detection)
    Algorithm 1 computes Ymin and Ymax as ycenter plus or minus 0.5 times the height of the first sorted box. The 0.5 factor is chosen by hand and not derived or cross-validated.
assumptions (3)
  • standard math YOLOv3 and Darknet-53 perform as described in the cited literature
    The paper relies entirely on the correctness and behavior of the YOLOv3 object detector and Darknet-53 backbone as published, without re-verification. Invoked in Section III-A.
  • domain assumption The Hishab dataset annotations are correct and representative of real handwritten Bengali math expressions
    All detection metrics are computed on this self-made dataset, and no annotation quality check, inter-annotator agreement, or external validation is provided. Invoked in Sections III-B and IV.
  • ad hoc to paper Simple horizontal grouping with vertical-overlap suffices to parse mathematical expressions
    Algorithm 1 sorts detections by x-center and groups by vertical overlap with the first box, assuming all expressions are horizontally arranged and that no structural layout (fractions, exponents, nested brackets) needs to be modeled. This assumption is not validated.

how reviews work

0 comments
Cite this review

Pith. "Pith review of HishabNet: Detection, Localization and Calculation of Handwritten Bengali Mathematical Expressions." pith.science (2026). https://pith.science/paper/W5BSNG7Z

@misc{pith2026190900823,
  author       = {Pith},
  title        = {Pith review of: HishabNet: Detection, Localization and Calculation of Handwritten Bengali Mathematical Expressions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W5BSNG7Z}},
  note         = {Machine review of arXiv:1909.00823}
}
read the original abstract

Recently, recognition of handwritten Bengali letters and digits have captured a lot of attention among the researchers of the AI community. In this work, we propose a Convolutional Neural Network (CNN) based object detection model which can recognize and evaluate handwritten Bengali mathematical expressions. This method is able to detect multiple Bengali digits and operators and locate their positions in the image. With that information, it is able to construct numbers from series of digits and perform mathematical operations on them. For the object detection task, the state-of-the-art YOLOv3 algorithm was utilized. For training and evaluating the model, we have engineered a new dataset 'Hishab' which is the first Bengali handwritten digits dataset intended for object detection. The model achieved an overall validation mean average precision (mAP) of 98.6%. Also, the classification accuracy of the feature extractor backbone CNN used in our model was tested on two publicly available Bengali handwritten digits datasets: NumtaDB and CMATERdb. The backbone CNN achieved a test set accuracy of 99.6252% on NumtaDB and 99.0833% on CMATERdb.

Figures

Figures reproduced from arXiv: 1909.00823 by the authors.

Figure 1
Figure 1. Calculation of Intersection over Union Additionally, in a typical dataset there will be a lot of classes and the distribution of these classes might not be uniform. So, a simple accuracy-based metric can introduce biases in the evaluation. It is also essential to determine the likelihood of misclassifications. Thus, it is imperative to assign a confidence score with each detected bounding box and to analyze the mode… view at source ↗
Figure 2
Figure 2. The overall architecture of the proposed YOLOv3 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. A subset of our dataset C. Training During training, we used batch gradient descent with a batch size of 64 images. The model was trained for 40000 iterations where each iteration is a batch gradient descent step using 64 images. This means we have trained for 64 epochs as our dataset consists of 40000 images. We utilized an SGD optimizer with an initial learning rate of 0.001, [PITH_FULL_IMAGE:figures/full_fig_p00… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Plot of Average Training Loss and Overall Validation [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Different detection outputs for our system [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 24 canonical work pages

  1. [1]

    Yolov3: An incremental improvement,

    J. Redmon and A. Farhadi, “Yolov3: An incremental improvement,” arXiv preprint arXiv:1804.02767 , 2018

    arXiv 2018

  2. [2]

    You only look once: Unified, real-time object detection,

    J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, “You only look once: Unified, real-time object detection,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp. 779– 788

    work page 2016

  3. [3]

    Segmentation and recognition system for unknown-length handwritten digit strings,

    A. Gattal, Y . Chibani, and B. Hadjadji, “Segmentation and recognition system for unknown-length handwritten digit strings,”Pattern Analysis and Applications, vol. 20, no. 2, pp. 307–323, 2017

    work page 2017

  4. [4]

    Handwritten digit recognition: benchmarking of state-of-the-art techniques,

    C.-L. Liu, K. Nakashima, H. Sako, and H. Fujisawa, “Handwritten digit recognition: benchmarking of state-of-the-art techniques,” Pat- tern recognition, vol. 36, no. 10, pp. 2271–2285, 2003

    work page 2003

  5. [5]

    Handwritten digit recognition using rotations,

    A. Ignat and B. Aciobanitei, “Handwritten digit recognition using rotations,” in 2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2016, pp. 303–306

    work page 2016

  6. [6]

    Permutative coding technique for hand- written digit recognition system,

    E. Kussul and T. Baidyk, “Permutative coding technique for hand- written digit recognition system,” in Proceedings of the International Joint Conference on Neural Networks, 2003. , vol. 3. IEEE, 2003, pp. 2163–2168

    work page 2003

  7. [7]

    A comparative study on hand- writing digit recognition using neural networks,

    M. M. A. Ghosh and A. Y . Maghari, “A comparative study on hand- writing digit recognition using neural networks,” in 2017 International Conference on Promising Electronic Technologies (ICPET) . IEEE, 2017, pp. 77–81

    work page 2017

  8. [8]

    Handwritten digit recognition using machine learning algorithms,

    S. Shamim, M. B. A. Miah, A. Sarker, M. Rana, and A. Al Jobair, “Handwritten digit recognition using machine learning algorithms,” Global Journal Of Computer Science And Technology , 2018

    work page 2018

Show all 28 references
  1. [9]

    Icdar 2013 chinese handwriting recognition competition,

    F. Yin, Q.-F. Wang, X.-Y . Zhang, and C.-L. Liu, “Icdar 2013 chinese handwriting recognition competition,” in 2013 12th International Conference on Document Analysis and Recognition . IEEE, 2013, pp. 1464–1470

    2013

  2. [10]

    Off-line arabic character recognition: the state of the art,

    A. Amin, “Off-line arabic character recognition: the state of the art,” Pattern recognition, vol. 31, no. 5, pp. 517–530, 1998

    1998

  3. [11]

    The gruhd database of greek unconstrained handwrit- ing,

    E. Kavallieratou, N. Liolios, E. Koutsogeorgos, N. Fakotakis, and G. Kokkinakis, “The gruhd database of greek unconstrained handwrit- ing,” in Proceedings of Sixth International Conference on Document Analysis and Recognition . IEEE, 2001, pp. 561–565

    2001

  4. [12]

    A robust model for on-line handwritten japanese text recognition,

    B. Zhu, X.-D. Zhou, C.-L. Liu, and M. Nakagawa, “A robust model for on-line handwritten japanese text recognition,” International Journal on Document Analysis and Recognition (IJDAR) , vol. 13, no. 2, pp. 121–131, 2010

    2010

  5. [13]

    Numeral script identification from handwritten document images,

    S. M. Obaidullah, C. Halder, N. Das, and K. Roy, “Numeral script identification from handwritten document images,” Procedia Com- puter Science, vol. 54, pp. 585–594, 2015

    2015

  6. [14]

    Handwritten bangla digit recognition using chemical reaction optimization,

    P. K. Boni, B. S. Abir, H. M. Hasan, and M. R. Islam, “Handwritten bangla digit recognition using chemical reaction optimization,” in 2018 9th International Conference on Computing, Communication and Networking Technologies (ICCCNT). IEEE, 2018, pp. 1–7

    2018

  7. [15]

    Bornonet: Bangla handwritten characters recognition using convo- lutional neural network,

    A. S. A. Rabby, S. Haque, S. Islam, S. Abujar, and S. A. Hossain, “Bornonet: Bangla handwritten characters recognition using convo- lutional neural network,” Procedia computer science , vol. 143, pp. 528–535, 2018

    2018

  8. [16]

    A new neural network based algorithm for identifying handwritten mathematical equations,

    S. Shinde, R. Waghulade, and D. Bormane, “A new neural network based algorithm for identifying handwritten mathematical equations,” in 2017 International Conference on Trends in Electronics and Infor- matics (ICEI). IEEE, 2017, pp. 204–209

    2017

  9. [17]

    Recognition of online handwritten mathematical expressions,

    U. Garain and B. B. Chaudhuri, “Recognition of online handwritten mathematical expressions,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) , vol. 34, no. 6, pp. 2366–2376, 2004

    2004

  10. [18]

    A real-time recognition system for hand- written mathematics: Structural development,

    R. Genoe and T. Kechadi, “A real-time recognition system for hand- written mathematics: Structural development,” in 2010 12th Interna- tional Conference on Frontiers in Handwriting Recognition . IEEE, 2010, pp. 593–598

    2010

  11. [19]

    Offline handwritten mathematical expression recognition using convolutional neural network,

    L. Dsouza and M. Mascarenhas, “Offline handwritten mathematical expression recognition using convolutional neural network,” in 2018 International Conference on Information, Communication, Engineer- ing and Technology (ICICET) . IEEE, 2018, pp. 1–3

    2018

  12. [20]

    Darknet: Open source neural networks in c,

    J. Redmon, “Darknet: Open source neural networks in c,” 2013–2016

    2013

  13. [21]

    Rich feature hierarchies for accurate object detection and semantic segmentation,

    R. Girshick, J. Donahue, T. Darrell, and J. Malik, “Rich feature hierarchies for accurate object detection and semantic segmentation,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2014, pp. 580–587

    2014

  14. [22]

    Fast r-cnn,

    R. Girshick, “Fast r-cnn,” in The IEEE International Conference on Computer Vision (ICCV) , December 2015

    2015

  15. [23]

    Faster r-cnn: Towards real- time object detection with region proposal networks,

    S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn: Towards real- time object detection with region proposal networks,” in Advances in Neural Information Processing Systems 28 , 2015, pp. 91–99

    2015

  16. [24]

    Ssd: Single shot multibox detector,

    W. Liu, D. Anguelov, D. Erhan, C. Szegedy, S. Reed, C.-Y . Fu, and A. C. Berg, “Ssd: Single shot multibox detector,” in European conference on computer vision . Springer, 2016, pp. 21–37

    2016

  17. [25]

    Focal loss for dense object detection,

    T.-Y . Lin, P. Goyal, R. Girshick, K. He, and P. Doll ´ar, “Focal loss for dense object detection,” in Proceedings of the IEEE international conference on computer vision , 2017, pp. 2980–2988

    2017

  18. [26]

    Yolo9000: better, faster, stronger,

    J. Redmon and A. Farhadi, “Yolo9000: better, faster, stronger,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2017, pp. 7263–7271

    2017

  19. [27]

    Numtadb - assembled bengali handwritten digits,

    S. Alam, T. Reasat, R. M. Doha, and A. I. Humayun, “Numtadb - assembled bengali handwritten digits,” CoRR, vol. abs/1806.02452, 2018

    2018 arXiv

  20. [28]

    A genetic algorithm based region sampling for selection of local features in handwritten digit recognition application,

    N. Das, R. Sarkar, S. Basu, M. Kundu, M. Nasipuri, and D. K. Basu, “A genetic algorithm based region sampling for selection of local features in handwritten digit recognition application,” Appl. Soft Comput., vol. 12, no. 5, pp. 1592–1606, May 2012

    2012

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.