This repository contains the code and resources for the papers: "Minimum length in the tangent bundle as a model for curve completion" CVPR 2010 and "A Tangent Bundle Theory for Visual Curve Completion" PAMI 2012. These papers introduce a mathematical framework for curve completion using the concept of minimum length in the tangent bundle.

The Minimum Length in the Tangent Bundle (MLTB) framework provides a biologically inspired approach to visual curve completion. It models curves in the tangent bundle and computes the shortest path that satisfies constraints in a geometric manifold, abstracting the structure of the early visual cortex and drawing inspiration from biological processes in human vision. This repository includes implementations of the model, experiments, and visualizations to support the concepts introduced in the papers.

To install the required dependencies, run:

pip install -r requirements.txt

The main functionality is provided in the mltb.py file located in the src directory. You can use the functions defined in this file to perform curve completion tasks.

To see example usage, check the MLTB_Examples.ipynb file in the notebooks/ directory. This file demonstrates how to compute and visualize curve completions using the MLTB framework.

For more details on the mathematical framework and applications, refer to the original papers:

• Guy Ben-Yosef, Ohad Ben-Shahar, "Minimum length in the tangent bundle as a model for curve completion", IEEE Computer Vision and Pattern Recognition (CVPR), 2010, (oral presentation).
• Guy Ben-Yosef, Ohad Ben-Shahar, "A Tangent Bundle Theory for Visual Curve Completion", IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2012.

Other related papers on tangent bundle theory:

• Ohad Ben-Shahar, Guy Ben-Yosef, "Tangent Bundle Elastica and Computer Vision", IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2014.
• Guy Ben-Yosef, Ohad Ben-Shahar, "Tangent Bundle Curve Completion with Locally Connected Parallel Networks", Neural Computation, 2012.
• Guy Ben-Yosef, Ohad Ben-Shahar, "A Biologically-Inspired Theory for Non-axiomatic Parametric Curve Completion", Asian Conference on Computer Vision (ACCV), 2010.

If you use this code in your research, please cite the papers:

@inproceedings{mltb_cvpr2010,
    title={Minimum length in the tangent bundle as a model for curve completion},
    author={Ben-Yosef, Guy and Ben-Shahar, Ohad},
    booktitle={IEEE Computer Vision and Pattern Recognition (CVPR)},
    pages={1--8},
    year={2010},
    organization={IEEE}
}

@article{mltb_pami2012,
    title={A Tangent Bundle Theory for Visual Curve Completion},
    author={Ben-Yosef, Guy and Ben-Shahar, Ohad},
    journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
    volume={34},
    number={7},
    pages={1263--1280},
    year={2012},
    publisher={IEEE}
}

For a detailed implementation of the Elastica in the Tangent Bundle (ETB) model, please visit the following repository:

• Elastica in the Tangent Bundle (ETB): This repository provides the code and resources for the Elastica in the Tangent Bundle model, as described in the related paper: "Tangent Bundle Elastica and Computer Vision" (PAMI 2014). It includes implementations of the model, experiments, and visualizations.