OCR of Mathematical Formulas: Pix2Tex, Mathpix, TrOCR

Imagine a scanned article with integrals, matrices, and summations — standard OCR output is gibberish. The two-dimensional structure of formulas, exponents, fraction lines, and special symbols (∫, ∑, ∂, ∞) don't fit into a linear text recognition model. You need the result in LaTeX or MathML for typesetting, analysis, or publication. Our custom formula recognition using Pix2Tex and Mathpix achieves up to 93% BLEU on standard benchmarks. Over 5+ years, we've completed more than 20 projects in this area, accumulating experience to handle tasks of any complexity.

We develop industrial formula OCR systems that convert images and PDFs into mathematical markup. Our clients include publishers, EdTech platforms, and research labs — from simple single-line equations to multi-line theorems.

Why formula recognition is harder than regular OCR

A formula isn't a string of characters; it's a graph with rigid positional relationships. Problems: overlapping characters (superscripts/subscripts), fractions without explicit delimiters, matrices with gaps, handwritten symbols with variability. Misrecognizing an integral or a limit boundary can completely change the meaning. That's why we use specialized models, not general-purpose OCR.

How we do it: stack and case study

For one EdTech project, we built a pipeline: formula segmentation → recognition using Pix2Tex → validation by LaTeX compilation → post-processing with an LLM to fix grammar errors (fine-tuned LLaMA 3 on a LaTeX dataset). This reduced non-compilable formulas from 12% to 1.5%. Stack: YOLOv8 for detection, Pix2Tex as the base recognizer, Hugging Face Transformers, pdflatex for validation.

Pix2Tex: LaTeX OCR from images

from pix2tex.cli import LatexOCR
from PIL import Image

class FormulaRecognizer:
    def __init__(self):
        self.model = LatexOCR()

    def recognize(self, image_path: str) -> dict:
        img = Image.open(image_path)
        latex = self.model(img)

        return {
            'latex': latex,
            'rendered': self._latex_to_mathml(latex)
        }

    def _latex_to_mathml(self, latex: str) -> str:
        try:
            import latex2mathml.converter
            return latex2mathml.converter.convert(latex)
        except Exception:
            return ''

recognizer = FormulaRecognizer()
result = recognizer.recognize('equation.png')
print(result['latex'])  # \frac{d}{dx}\left(x^2\right) = 2x

Alternative: Mathpix API

Mathpix is a commercial service with the best recognition quality on complex multi-line formulas and mixed-content texts:

import requests
import base64
import json

class MathpixOCR:
    def __init__(self, app_id: str, app_key: str):
        self.app_id = app_id
        self.app_key = app_key
        self.url = 'https://api.mathpix.com/v3/text'

    def recognize_formula(self, image_path: str) -> dict:
        with open(image_path, 'rb') as f:
            image_b64 = base64.b64encode(f.read()).decode()

        response = requests.post(
            self.url,
            headers={
                'app_id': self.app_id,
                'app_key': self.app_key,
                'Content-Type': 'application/json'
            },
            json={
                'src': f'data:image/jpeg;base64,{image_b64}',
                'formats': ['text', 'latex_styled', 'mathml'],
                'math_inline_delimiters': ['$', '$'],
                'math_display_delimiters': ['$$', '$$']
            }
        )

        data = response.json()
        return {
            'latex': data.get('latex_styled', ''),
            'text': data.get('text', ''),
            'mathml': data.get('mathml', ''),
            'confidence': data.get('confidence', 0)
        }

Custom model based on TrOCR

For specific notations (chemical formulas, physical symbols) we fine-tune TrOCR on your dataset:

from transformers import VisionEncoderDecoderModel, TrOCRProcessor

model = VisionEncoderDecoderModel.from_pretrained('microsoft/trocr-base-stage1')
processor = TrOCRProcessor.from_pretrained('microsoft/trocr-base-stage1')
# Fine-tuning on latex_pairs: [(image, latex_string), ...]

How to choose between Pix2Tex and Mathpix?

Pix2Tex wins on speed: it's 2–4 times faster than Mathpix (0.3–0.7 sec on GPU vs 1–2 sec) and fully local — no internet required. Mathpix provides higher accuracy (93+ BLEU vs 87.3), especially on handwritten formulas (85% vs 72%) and complex layouts. If privacy is important and accuracy requirements are moderate, go with Pix2Tex. For high-load publishing systems with strict quality demands, choose Mathpix. We help you decide and, if needed, combine both approaches: Pix2Tex for fast preview, Mathpix for final polishing.

What is formula segmentation and why is it needed?

Before recognizing formulas, you need to locate them in a document. Two approaches:

• Formula detector: YOLOv8 fine-tuned on a dataset of documents with labeled formulas (inline and display). mAP > 0.90 on the test set.
• PDF via PyMuPDF: extracting formula blocks by parsing the PDF structure (for digitally created PDFs).

Validation through LaTeX compilation

We automatically verify the correctness of recognized formulas by compiling with pdflatex:

import subprocess
import tempfile
import os

def validate_latex(latex: str) -> bool:
    template = r"""
    \documentclass{article}
    \usepackage{amsmath}
    \begin{document}
    $""" + latex + r"""$
    \end{document}
    """
    with tempfile.NamedTemporaryFile(suffix='.tex', mode='w', delete=False) as f:
        f.write(template)
        tex_path = f.name

    try:
        result = subprocess.run(
            ['pdflatex', '-interaction=nonstopmode', tex_path],
            capture_output=True, timeout=10
        )
        return result.returncode == 0
    except Exception:
        return False
    finally:
        os.unlink(tex_path)

Process of evaluation and work

1. Analysis: measure data volume, formula types, accuracy requirements, latency constraints.
2. Approach selection: Pix2Tex, Mathpix, or custom model (TrOCR + LoRA).
3. Integration: embed the pipeline into your infrastructure (Docker, API, message brokers).
4. Testing: validation on a test set, A/B testing.
5. Deployment: rollout with monitoring (latency p99, accuracy) and CI/CD.

What's included in the work

• Architecture and API documentation.
• Training workshop for your team.
• 3 months of support: bug fixes, model updates, consultations.

Orientation on timelines

Pricing for typical projects ranges from $5,000 to $50,000, with a free initial assessment. Cost is determined individually. Contact us to evaluate your project. We guarantee accuracy no less than 90% on your corpus after calibration and provide certified engineers with experience in OCR and MLOps. Get a consultation: write to us, and we'll review your case.

Pix2Tex: Lukas Blecher, "Pix2Tex: LaTeX OCR from images", GitHub repository.

How Distribution Shift Kills CV Model Metrics in Industry

On a production line, a camera is installed to control product quality. The model is trained on 10,000 labeled images—test accuracy mAP 0.84. Deployed to production, and in the first week it misses 30% of defects. Lighting on the line changes between shifts; distribution shift nullifies the metrics. This is a classic story with computer vision in industry, where pattern recognition fails without proper drift handling.

Our engineers, with experience from 60+ computer vision projects, know how to eliminate such scenarios. We guarantee stable model performance under real conditions.

Object Detection: YOLO, RT-DETR, and Everything in Between

YOLO is the standard for real-time detection. YOLOv8 and YOLOv11 from Ultralytics are the most used versions in production: simple API, active community, built-in validation, and export to ONNX/TensorRT. For tasks with high accuracy requirements and less critical latency, RT-DETR, a transformer-based architecture without NMS, gives better mAP on COCO at comparable speed to YOLOv8l.

A typical mistake when training a detector: dataset of 8000 images, 3 classes, fine-tune YOLOv8m—F1 0.73 on validation. Look at confusion matrix—one class is almost never detected. Cause: imbalance 1:23. Solution: oversampling rare class, focal loss for objectness, augmentations (Mosaic, MixUp disabled for rare class as they "blur" it). Transfer learning is mandatory: pretrained on COCO weights reduces data requirement by 10 times. Fine-tuning on 500–2000 domain images yields a working model in 1–2 days on a single GPU.

For edge deployment: export to ONNX → TensorRT engine. YOLOv8n in TensorRT FP16 on Jetson AGX Orin gives 150+ FPS at P99 latency < 8 ms—3 times faster than ONNX Runtime without TensorRT. On server A10G: 700+ FPS for YOLOv8n in TensorRT INT8.

How Does Fine-Tuning YOLO Help in Pattern Recognition?

Suppose you need to find micro-defects on a metal surface—a task with high resolution and class imbalance. We use YOLOv8m pretrained on COCO and fine-tune on 2000 proprietary images. Apply augmentations Mosaic, MixUp, random perspective. After 200 epochs, mAP 0.5 reaches 0.93. Key techniques:

• Focal loss for the objectness head—reduces contribution of easily classified examples.
• Class-balanced sampling—equalizes representation of rare classes.
• Test Time Augmentation (TTA)—increases recall by 5–7% through averaging over flips and scales.

Get a consultation on architecture selection for your task—contact us.

Segmentation: SAM, Mask R-CNN, and Instance Segmentation

SAM (Segment Anything Model) from Meta changed the approach to segmentation. SAM 2 works with video, supports object tracking across frames—for interactive object selection by point or bbox, it's the best out-of-the-box choice. For production instance segmentation without interactive prompting, Mask R-CNN or YOLOv8-seg are used. YOLOv8-seg trains like a regular detector with additional masks, convenient in the same pipelines. Semantic segmentation (each pixel is a class) uses SegFormer, DeepLabV3+. SegFormer-B5 provides a good balance of accuracy and speed for satellite imagery or medical segmentation.

Case study: cell segmentation on microscopic images. Dataset of 400 images with manual annotation. Training Mask R-CNN on ResNet-50 backbone gave IoU 0.61—poor. Problem: objects (cells) overlap; standard NMS kills overlapping predictions. Solution: switch to cellpose (specialized architecture for biomedical tasks) + soft-NMS. IoU increased to 0.79.

OCR: When Tesseract Fails

Tesseract is a starting point for simple tasks: printed text, good lighting, straight layout. As soon as there are handwritten elements, non-standard fonts, perspective distortions, or multi-column layouts, Tesseract degrades quickly.

PaddleOCR is a production-grade solution: text block detection + recognition + structural analysis. Works out of the box for 80+ languages, including Russian. Supports tables and complex document structures. TrOCR (Microsoft) is a transformer OCR with strong results on handwritten text. For Russian handwritten text, fine-tuning is needed: the base model is trained mostly on Latin script.

What to Do When Tesseract Cannot Handle Pattern Recognition on Documents?

For tasks like "extract data from invoices/contracts/passports," we use LayoutLMv3 or Donut—these models understand document layout, not just text. Integration via Hugging Face Transformers, fine-tuning on 200–500 annotated documents. Typical pipeline:

1. Preprocessing: deskew, denoising, binarization via OpenCV.
2. Text block detection: PaddleOCR detection or CRAFT.
3. Recognition: PaddleOCR recognition or TrOCR.
4. Post-processing: normalization, validation via regex or LLM for structured fields.

For documents with fixed structure, template matching + OCR by coordinates is often more reliable than an end-to-end solution.

Face Recognition: Identification and Verification

Face recognition = detection + alignment + embedding + matching. Each stage matters.

Detection: RetinaFace or InsightFace for accurate face localization and keypoints. MTCNN is older but reliable. Embedding: ArcFace (InsightFace) is state-of-the-art for face recognition embeddings. Models iresnet50/iresnet100 pretrained on MS1MV3 (5M identities). Embedding vector 512 float32, comparison by cosine similarity. Threshold tuning: decision threshold is a critical parameter. At threshold 0.6, typical FPR on LFW benchmark is 0.001, TPR is 0.985. In production, threshold must be calibrated to the real distribution: people in masks, with changed appearance, different lighting conditions. Liveness detection is mandatory: MiniFASNet—lightweight model on CPU; FaceX-Zoo contains several pretrained liveness detectors.

Video Analytics

Video is a sequence of frames plus a temporal dimension. A naive approach—detecting on every frame—is expensive.

Tracking: ByteTrack and BoT-SORT are the standard for multi-object tracking. They work on top of any detector, adding persistent IDs to objects across frames—enabling object counting, motion tracking, velocity.

Optimization: not every frame needs processing. For static scenes, detect every 5–10 frames, with tracking in between. For event detection (person entering a zone), background subtraction (OpenCV MOG2) serves as a lightweight pre-filter before neural detection. Action recognition: SlowFast, VideoMAE for action classification. Heavy models—for production use ONNX export + TensorRT or offline processing.

How to Measure Pattern Recognition Model Quality in Production?

Quality monitoring is key to MLOps. We track:

• Prediction confidence distribution.
• Share of low-confidence predictions (indicator of OOD data).
• Drift of input images via feature distribution (embeddings from backbone).

A drop in average confidence from 0.87 to 0.71 over a week is an early signal of distribution shift. NVIDIA Triton Inference Server recommends tracking these metrics via Prometheus. Our certified engineers set up monitoring and guarantee SLA for inference quality.

Deployment of CV Models

For online inference, we use Triton Inference Server (NVIDIA)—production standard for serving CV models. Supports TensorRT, ONNX, PyTorch, dynamic batching, multiple instances. REST and gRPC API. We guarantee stable operation under load.

Edge deployment: ONNX Runtime on ARM/x86 CPU. TensorFlow Lite for mobile devices. OpenVINO for Intel CPU/GPU/VPU—gives 2–3× speedup on Intel hardware compared to ONNX Runtime. After deployment, we hand over the model with documentation and train personnel.

What Is Included in the Work

Deadlines and Cost

A prototype detector on existing data takes 1–2 weeks. Production system with optimization for target hardware takes 4–8 weeks. Full cycle including data labeling (1000–5000 images) takes 2–4 months. Cost is calculated individually for each task. Typical savings from implementing a quality control system can be significant per production line.

We have been in the market for over 5 years and completed 60+ computer vision projects. We will evaluate your project end-to-end—request a consultation to get a quote and technical proposal.