Fast General Norm Approximation

Description

This is a Python implementation of a solver for the following minimization problem:

based on my work on "Fast General Norm Approximation via Iteratively Reweighted Least Squares" presented in The 4th ACCV workshop on e-Heritage 2016.

Installation

Put general_norm.py in your directory. This program requires

• Python 3.5
• Numpy
• Scipy
• opencv (for reading images in photometric_stereo.py)

Usage

from general_norm import GeneralNorm
m = GeneralNorm(list_A, list_b, w, p)
x = m.solve()

list_A is a list of scipy sparse matrices A, list_b is a list of numpy ndarray b, w is a numpy array of weights on norms, and p is a numpy array of p values in l_p norms. We can get x as solution of the minimization problem.

Example

random_norm.py

Design matrices A and solution x are randomly determined, and b is calculated by A x. Then the problem to minimize the sum of norms ||A x - b||_p^p is solved with respect to x.

photometric_stereo.py

Normal map N of an object is estimated from measurement M and light direction L based on Lambert's law. This program can receive either point cloud with normals or measurement images of an object under different light directions.

sfn.py

Surface represented by a set of depth is estimated from normal map N based on the fact that differentiation of the surface is corresponding to gradient, which can be calculated from normal.