====== RIDL-Hex is an efficient sparse dictionary learning algorithm for extracting rotation-aware or rotation-invariant features from images. RIDL-Hex benefits from a novel hexagonal sampling grid, a modified rotation-invariant sparse coding (based on Orthogonal Matching Pursuit) and a rotation learning algorithm, based on an exponentiated-gradient algorithm, for updating the dictionary matrix. The dictionary elements in RIDL-Hex are parametrized by their orientation, and a wide range of patterns can be well represented with a small dictionary size. RIDL-Hex achieves faster convergence than other dictionary learning algorithms not using this type of parameterization.

This implementation of RIDL-Hex is based on python 2.7 and requires following python packages:

Main dependencies:

• numpy
• scipy
• matplotlib

and limited usage of

• opencv (in order to load image files)
• pillow (used in creating a circular mask for square grid)
• scikit-learn (used in efficient shuffling of the data matrix)

Since calculating norms of columns of a matrix is a feature added in numpy 1.8, you need to have numpy 1.8 or newer. This code is tested on:

• scipy (0.12.1)
• numpy (1.10.4)
• opencv (2.4.5)
• pillow (2.0.)
• matplotlib (1.2.0)
• scikit-learan (0.17)

• foveated_sampling.py creates a foveated samples from an image and displays the hexagonal grid structure used in foveated sampling

• dict_learning_comp_sgd.py compares the convergence of reconstruction error for dictionary learning using stochastic gradient descent for rotation invariant and dictionary matrix with independent elements for different grid structures.

• dict_learning_comp_rotation_update.py compares the convergence of reconstruction error for dictionary learning using rotation learning for rotation invariant and dictionary matrix with independent elements for different grid strctures.

• activation_patterns_dict_elements.py learns a rotation invariant dictionary for three images (Lena, Barbara and a Van Gogh painting), and draws the pattern of usage of different orientations of each dictionary element.