Mixed Region Covariance Discriminative Learning for Image Classification on Riemannian Manifolds

Algorithm 1

Input:

(i) The mixed region covariance descriptors of the image regions for

training and the corresponding labels .

(ii) The number of images in the -th class , .

(iii) The mixed region covariance descriptor of the test image region.

Processing:

1: Calculate the matrix logarithm for all ,

2: for each point   do

3: for each point   do

4: Calculate the log-Euclidean distance between and (2),

5: end for

6: end for

7: Calculate the kernel matrix (13),

8: for each class   do

9: Calculate the mean (21) and the centralized matrix (22),

10: end for

11: Calculate the within-class scatter matrix (24),

12: Calculate the between-class scatter matrix (26),

13: Solve the eigen-problem: . The eigenvectors corresponding to the

largest eigenvalues of form ,

14: Calculate the projections of (19),

15: Calculate the projection of the testing matrix (18),

16: The label of the test region is determined by KNN classifier between and

Output:

(i) The class of the test region .