Filterbank responses for low level vision

filterbank.py

##########################################################################
# Maximum Response filterbank from
# http://www.robots.ox.ac.uk/~vgg/research/texclass/filters.html
# based on several edge and bar filters.
# Adapted to Python by Andreas Mueller amueller@ais.uni-bonn.de
# Share and enjoy
#

import numpy as np
import matplotlib.pyplot as plt
from itertools import product, chain
from scipy.misc import lena
#from sklearn.externals.joblib import Parallel, delayed


def makeRFSfilters(radius=24, sigmas=[1, 2, 4], n_orientations=6):
    """ Generates filters for RFS filterbank.

    Parameters
    ----------
    radius : int, default 28
        radius of all filters. Size will be 2 * radius + 1

    sigmas : list of floats, default [1, 2, 4]
        define scales on which the filters will be computed

    n_orientations : int
        number of fractions the half-angle will be divided in

    Returns
    -------
    edge : ndarray (len(sigmas), n_orientations, 2*radius+1, 2*radius+1)
        Contains edge filters on different scales and orientations
    bar : ndarray (len(sigmas), n_orientations, 2*radius+1, 2*radius+1)
        Contains bar filters on different scales and orientations
    rot : ndarray (2, 2*radius+1, 2*radius+1)
        contains two rotation invariant filters, Gaussian and Laplacian of
        Gaussian
    """
    def make_gaussian_filter(x, sigma, order=0):
        if order > 2:
            raise ValueError("Only orders up to 2 are supported")
        # compute unnormalized Gaussian response
        response = np.exp(-x ** 2 / (2. * sigma ** 2))
        if order == 1:
            response = -response * x
        elif order == 2:
            response = response * (x ** 2 - sigma ** 2)
        # normalize
        response /= np.abs(response).sum()
        return response

    def makefilter(scale, phasey, pts, sup):
        gx = make_gaussian_filter(pts[0, :], sigma=3 * scale)
        gy = make_gaussian_filter(pts[1, :], sigma=scale, order=phasey)
        f = (gx * gy).reshape(sup, sup)
        # normalize
        f /= np.abs(f).sum()
        return f

    support = 2 * radius + 1
    x, y = np.mgrid[-radius:radius + 1, radius:-radius - 1:-1]
    orgpts = np.vstack([x.ravel(), y.ravel()])

    rot, edge, bar = [], [], []
    for sigma in sigmas:
        for orient in xrange(n_orientations):
            # Not 2pi as filters have symmetry
            angle = np.pi * orient / n_orientations
            c, s = np.cos(angle), np.sin(angle)
            rotpts = np.dot(np.array([[c, -s], [s, c]]), orgpts)
            edge.append(makefilter(sigma, 1, rotpts, support))
            bar.append(makefilter(sigma, 2, rotpts, support))
    length = np.sqrt(x ** 2 + y ** 2)
    rot.append(make_gaussian_filter(length, sigma=10))
    rot.append(make_gaussian_filter(length, sigma=10, order=2))

    # reshape rot and edge
    edge = np.asarray(edge)
    edge = edge.reshape(len(sigmas), n_orientations, support, support)
    bar = np.asarray(bar).reshape(edge.shape)
    rot = np.asarray(rot)[:, np.newaxis, :, :]
    return edge, bar, rot


def apply_filterbank(img, filterbank):
    from scipy.ndimage import convolve
    result = []
    for battery in filterbank:
        response = [convolve(img, filt) for filt in battery]
        #response = Parallel(n_jobs=5)(
                #delayed(convolve)(img, filt) for filt in battery)
        max_response = np.max(response, axis=0)
        result.append(max_response)
        print("battery finished")
    return result


if __name__ == "__main__":
    sigmas = [1, 2, 4]
    n_sigmas = len(sigmas)
    n_orientations = 6

    edge, bar, rot = makeRFSfilters(sigmas=sigmas,
            n_orientations=n_orientations)

    n = n_sigmas * n_orientations

    # plot filters
    # 2 is for bar / edge, + 1 for rot
    fig, ax = plt.subplots(n_sigmas * 2 + 1, n_orientations)
    for k, filters in enumerate([bar, edge]):
        for i, j in product(xrange(n_sigmas), xrange(n_orientations)):
            row = i + k * n_sigmas
            ax[row, j].imshow(filters[i, j, :, :], cmap=plt.cm.gray)
            ax[row, j].set_xticks(())
            ax[row, j].set_yticks(())
    ax[-1, 0].imshow(rot[0, 0], cmap=plt.cm.gray)
    ax[-1, 0].set_xticks(())
    ax[-1, 0].set_yticks(())
    ax[-1, 1].imshow(rot[1, 0], cmap=plt.cm.gray)
    ax[-1, 1].set_xticks(())
    ax[-1, 1].set_yticks(())
    for i in xrange(2, n_orientations):
        ax[-1, i].set_visible(False)

    # apply filters to lena
    img = lena().astype(np.float)
    filterbank = chain(edge, bar, rot)
    n_filters = len(edge) + len(bar) + len(rot)
    response = apply_filterbank(img, filterbank)
    # plot responses
    fig2, ax2 = plt.subplots(3, 3)
    for axes, res in zip(ax2.ravel(), response):
        axes.imshow(res, cmap=plt.cm.gray)
        axes.set_xticks(())
        axes.set_yticks(())
    ax2[-1, -1].set_visible(False)
    plt.show()