https://github.com/harusametime/generalnormapproximation

Fast General Norm Approximation via IRLS
https://github.com/harusametime/generalnormapproximation

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Fast General Norm Approximation via IRLS

• Host: GitHub
• URL: https://github.com/harusametime/generalnormapproximation
• Owner: harusametime
• Created: 2017-08-04T01:18:32.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2017-10-20T06:47:55.000Z (about 7 years ago)
• Last Synced: 2024-11-15T22:59:37.249Z (about 2 months ago)
• Language: Python
• Homepage:
• Size: 28.3 KB
• Stars: 0
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
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

```python

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.