LO09

Y. Li and S. Osher. A new median formula with applications to pde based denoising. Commun. Math, 7:741–753, 2009.

SRB10

D. Sun, S. Roth, and M. J. Black. Secrets of optical flow estimation and their principles. IEEE computer society conference on computer vision and pattern recognition., 17:2432–2439, 2010.

A. Src

Is a folder containaing the main python software sources.

Utils:

Utils imports the required functions and modules to run the code. The GPU version of the software will be privileged.

If Utils find some missing functions or modules the CPU version will be launched.

Precond:

Is used to compute the matrix-vector product of the inverse of the chosen preconditioner and a given vector.

This function will be used to create a matrix-free solver.

Solveur precond:

It’s a matrix-free implementation of Minres solver used in scipy.sparse and the function Minres of Matlab. This function is adapted to solve the following problem

\[P^{-1}Ax=P^{-1}b\]

Where \(A\) is the optical flow matrix, \(b\) the right hand term and \(P\) is the chosen preconditioner already defined in Precond file.

If we are handling \(N \times M\) images, then the problem has \(2\times N \times M\) as size.

The file contains also a function that computes the matrix-product of matrix of the problem and a given vector.

Flow operator:

The role of flow_operator module is the interpolation of the images using the current computed flow fields, the construction of the right hand term of the linear system and the definition of the base function for computing flow field that will be used at each level of the pyramid.

Compute flow:

Computes the optical flow fields using a pyramidal approach and the base function already defined in flow_operator.

Energies:

For computing the different energies described in the paper of D.Sun[.

Denoise LOnp:

Li and Osher [LO09] median filter implementation.

B. Test

To test the method we created a script able to read and modify the parameters of the algorithm using the sys.argv arguments. To run the script you can use ./mainscript, then you have to add at least three arguments:

  1. Path of the images folder

  2. Name of the first image of the sequence

  3. Name of the second image of the sequence

Syntax:

./mainscript /Give/The/Path/Folder  Im1.extension Im2.extension

To change the value of a desired parameter, you must add it after the executable using it’s key :

Table 2 Variables and their keys

Parameter

Keyword

Initial default value

Number of levels in the pyramid

pyram_levels

3

The downsampling factor

factor

2

The order of interpolation [Must be between 0 and 5]

ordre_inter

3
The size of the window used for Li and Osher

or the simple median filter

size_median_filter

5

Number of warping steps

max_iter

10

Maximum number of linearization performed per warping

max_linear_iter

1

Tikhonov Parameter

lmbda

3*10^4

Weight for coupling term

lambda2

0.001

Weight for non local term

lambda3

1

The name of the image Mask

Mask

None

Path for the mask image

Path_Mask

—

Syntax :

./mainscript /Give/The/Path/Folder  Im1.extension Im2.extension  keyword=new_value
   Mask=Mask.extension Path_Mask=/Path/Folder/OfMask

C. Images

In order to test the software, three image sequences and some masks with different shapes were given in this folder.