LEARNING-BASED PARTIAL DIFFERENTIAL EQUATIONS FOR COMPUTER VISION

摘要

Partial differential equations (PDEs) are used in the invention for various problems in computer the vision space. The present invention provides a framework for learning a system of PDEs from real data to accomplish a specific vision task. In one embodiment, the system consists of two PDEs. One controls the evolution of the output. The other is for an indicator function that helps collect global information. Both PDEs are coupled equations between the output image and the indicator function, up to their second order partial derivatives. The way they are coupled is suggested by the shift and rotational invariance that the PDEs should hold. The coupling coefficients are learnt from real data via an optimal control technique. The invention provides learning-based PDEs that make a unified framework for handling different vision tasks, such as edge detection, denoising, segementation, and object detection.