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.