diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt index 5feb5777..43c559b8 100644 --- a/CONTRIBUTORS.txt +++ b/CONTRIBUTORS.txt @@ -68,3 +68,8 @@ - Andreas Mueller Example data set loader. +- Brian Holt + Histograms of Oriented Gradients + +- David-Warde Farley, Sturla Molden + Bresenheim line drawing, from snippets on numpy-discussion. diff --git a/TASKS.txt b/TASKS.txt index 8c99a40a..1d32b373 100644 --- a/TASKS.txt +++ b/TASKS.txt @@ -122,3 +122,7 @@ Implement Algorithms - Graph cut segmentation - Probabilistic Hough transform +Drawing +``````` +- Wu's algorithm for lines and circles + diff --git a/scikits/image/draw/__init__.py b/scikits/image/draw/__init__.py new file mode 100644 index 00000000..907a1ba7 --- /dev/null +++ b/scikits/image/draw/__init__.py @@ -0,0 +1 @@ +from draw import * diff --git a/scikits/image/draw/_draw.pyx b/scikits/image/draw/_draw.pyx new file mode 100644 index 00000000..a586ae03 --- /dev/null +++ b/scikits/image/draw/_draw.pyx @@ -0,0 +1,66 @@ +import numpy as np +cimport numpy as np +cimport cython + +cdef extern from "math.h": + int abs(int i) + +@cython.boundscheck(False) +@cython.wraparound(False) +def bresenham(int y, int x, int y2, int x2): + """ + Generate line pixel coordinates. + + Parameters + ---------- + y, x : int + Starting position (row, column). + y2, x2 : int + End position (row, column). + + Returns + ------- + rr, cc : (N,) ndarray of int + Indices of pixels that belong to the line. + May be used to directly index into an array, e.g. + ``img[rr, cc] = 1``. + + """ + cdef np.ndarray[np.int32_t, ndim=1, mode="c"] rr, cc + + cdef int steep = 0 + cdef int dx = abs(x2 - x) + cdef int dy = abs(y2 - y) + cdef int sx, sy, d, i + + if (x2 - x) > 0: sx = 1 + else: sx = -1 + if (y2 - y) > 0: sy = 1 + else: sy = -1 + if dy > dx: + steep = 1 + x,y = y,x + dx,dy = dy,dx + sx,sy = sy,sx + d = (2 * dy) - dx + + rr = np.zeros(int(dx) + 1, dtype=np.int32) + cc = np.zeros(int(dx) + 1, dtype=np.int32) + + for i in range(dx): + if steep: + rr[i] = x + cc[i] = y + else: + rr[i] = y + cc[i] = x + while d >= 0: + y = y + sy + d = d - (2 * dx) + x = x + sx + d = d + (2 * dy) + + rr[dx] = y2 + cc[dx] = x2 + + return rr, cc diff --git a/scikits/image/draw/draw.py b/scikits/image/draw/draw.py new file mode 100644 index 00000000..9360623a --- /dev/null +++ b/scikits/image/draw/draw.py @@ -0,0 +1,6 @@ +""" +Methods to draw on arrays. + +""" + +from _draw import bresenham diff --git a/scikits/image/draw/setup.py b/scikits/image/draw/setup.py new file mode 100644 index 00000000..3e0cd1a4 --- /dev/null +++ b/scikits/image/draw/setup.py @@ -0,0 +1,30 @@ +#!/usr/bin/env python + +import os +from scikits.image._build import cython + +base_path = os.path.abspath(os.path.dirname(__file__)) + +def configuration(parent_package='', top_path=None): + from numpy.distutils.misc_util import Configuration, get_numpy_include_dirs + + config = Configuration('draw', parent_package, top_path) + config.add_data_dir('tests') + + cython(['_draw.pyx'], working_path=base_path) + + config.add_extension('_draw', sources=['_draw.c'], + include_dirs=[get_numpy_include_dirs()]) + + return config + +if __name__ == '__main__': + from numpy.distutils.core import setup + setup(maintainer = 'Scikits-image developers', + author = 'Scikits-image developers', + maintainer_email = 'scikits-image@googlegroups.com', + description = 'Drawing', + url = 'https://github.com/scikits-image/scikits.image', + license = 'SciPy License (BSD Style)', + **(configuration(top_path='').todict()) + ) diff --git a/scikits/image/draw/tests/test_draw.py b/scikits/image/draw/tests/test_draw.py new file mode 100644 index 00000000..06ebaac0 --- /dev/null +++ b/scikits/image/draw/tests/test_draw.py @@ -0,0 +1,52 @@ +from numpy.testing import assert_array_equal +import numpy as np + +from scikits.image.draw import bresenham + +def test_bresenham_horizontal(): + img = np.zeros((10, 10)) + + rr, cc = bresenham(0, 0, 0, 9) + img[rr, cc] = 1 + + img_ = np.zeros((10, 10)) + img_[0, :] = 1 + + assert_array_equal(img, img_) + +def test_bresenham_vertical(): + img = np.zeros((10, 10)) + + rr, cc = bresenham(0, 0, 9, 0) + img[rr, cc] = 1 + + img_ = np.zeros((10, 10)) + img_[:, 0] = 1 + + assert_array_equal(img, img_) + +def test_reverse(): + img = np.zeros((10, 10)) + + rr, cc = bresenham(0, 9, 0, 0) + img[rr, cc] = 1 + + img_ = np.zeros((10, 10)) + img_[0, :] = 1 + + assert_array_equal(img, img_) + +def test_diag(): + img = np.zeros((5, 5)) + + rr, cc = bresenham(0, 0, 4, 4) + img[rr, cc] = 1 + + img_ = np.eye(5) + + assert_array_equal(img, img_) + + +if __name__ == "__main__": + from numpy.testing import run_module_suite + diff --git a/scikits/image/feature/__init__.py b/scikits/image/feature/__init__.py new file mode 100644 index 00000000..eb6faa62 --- /dev/null +++ b/scikits/image/feature/__init__.py @@ -0,0 +1 @@ +from hog import hog \ No newline at end of file diff --git a/scikits/image/feature/hog.py b/scikits/image/feature/hog.py new file mode 100644 index 00000000..8b71f8a3 --- /dev/null +++ b/scikits/image/feature/hog.py @@ -0,0 +1,193 @@ +import numpy as np +from scipy import sqrt, pi, arctan2, cos, sin + +# XXX Replace with integral after merge +from ..transform import sat_sum + +def hog(image, orientations=9, pixels_per_cell=(8, 8), + cells_per_block=(3, 3), visualise=False, normalise=False): + """Extract Histogram of Oriented Gradients (HOG) for a given image. + + Compute a Histogram of Oriented Gradients (HOG) by + 1) (optional) global image normalisation + 2) computing the gradient image in x and y + 3) computing gradient histograms + 3) normalising across blocks + 4) flattening into a feature vector + + Parameters + ---------- + image : (M, N) ndarray + Input image (greyscale). + orientations : int + Number of orientation bins. + pixels_per_cell : 2 tuple (int, int) + Size (in pixels) of a cell. + cells_per_block : 2 tuple (int,int) + Number of cells in each block. + visualise : bool, optional + Also return an image of the HOG. + normalise : bool, optional + Apply power law compression to normalise the image before + processing. + + Returns + ------- + newarr : ndarray + HOG for the image as a 1D (flattened) array. + hog_image : ndarray (if visualise=True) + A visualisation of the HOG image. + + References + ---------- + * http://en.wikipedia.org/wiki/Histogram_of_oriented_gradients + + * Dalal, N and Triggs, B, Histograms of Oriented Gradients for + Human Detection, IEEE Computer Society Conference on Computer + Vision and Pattern Recognition 2005 San Diego, CA, USA + + """ + image = np.atleast_2d(image) + + """ + The first stage applies an optional global image normalisation + equalisation that is designed to reduce the influence of illumination + effects. In practice we use gamma (power law) compression, either + computing the square root or the log of each colour channel. + Image texture strength is typically proportional to the local surface + illumination so this compression helps to reduce the effects of local + shadowing and illumination variations. + """ + + if image.ndim > 3: + raise ValueError("Currently only supports grey-level images") + + if normalise: + image = sqrt(image) + + """ + The second stage computes first order image gradients. These capture + contour, silhouette and some texture information, while providing + further resistance to illumination variations. The locally dominant + colour channel is used, which provides colour invariance to a large + extent. Variant methods may also include second order image derivatives, + which act as primitive bar detectors - a useful feature for capturing, + e.g. bar like structures in bicycles and limbs in humans. + """ + + gx = np.zeros(image.shape) + gy = np.zeros(image.shape) + gx[:, :-1] = np.diff(image, n=1, axis=1) + gy[:-1, :] = np.diff(image, n=1, axis=0) + + """ + The third stage aims to produce an encoding that is sensitive to + local image content while remaining resistant to small changes in + pose or appearance. The adopted method pools gradient orientation + information locally in the same way as the SIFT [Lowe 2004] + feature. The image window is divided into small spatial regions, + called "cells". For each cell we accumulate a local 1-D histogram + of gradient or edge orientations over all the pixels in the + cell. This combined cell-level 1-D histogram forms the basic + "orientation histogram" representation. Each orientation histogram + divides the gradient angle range into a fixed number of + predetermined bins. The gradient magnitudes of the pixels in the + cell are used to vote into the orientation histogram. + """ + + magnitude = sqrt(gx ** 2 + gy ** 2) + orientation = arctan2(gy, (gx + 1e-15)) * (180 / pi) + 90 + + # compute orientations integral images + integral_images = [] + for i in range(orientations): + #create new integral image for this orientation + # isolate orientations in this range + + temp_ori = np.where(orientation < 180 / orientations * (i + 1), + orientation, 0) + temp_ori = np.where(orientation >= 180 / orientations * i, + temp_ori, 0) + # select magnitudes for those orientations + cond2 = temp_ori > 0 + temp_mag = np.where(cond2, magnitude, 0) + + #compute integral image + integral = np.cumsum(np.cumsum(temp_mag, axis=0, dtype=float), + axis=1, dtype=float) + integral_images.append(integral) + + sx, sy = image.shape + cx, cy = pixels_per_cell + bx, by = cells_per_block + + n_cellsx = int(np.floor(sx // cx)) # number of cells in x + n_cellsy = int(np.floor(sy // cy)) # number of cells in y + + # now for each cell, compute the histogram + orientation_histogram = np.zeros((n_cellsx, n_cellsy, orientations)) + + radius = min(cx, cy) // 2 - 1 + hog_image = None + if visualise: + hog_image = np.zeros((sy, sx), dtype=float) + + for x in range(n_cellsx): + for y in range(n_cellsy): + for o in range(orientations): + # compute the histogram from integral image + orientation_histogram[x, y, o] = sat_sum(integral_images[o], + y * cy, + x * cx, + (y + 1) * cy - 1, + (x + 1) * cx - 1) + + if visualise: + from scikits.image import draw + + for x in range(n_cellsx): + for y in range(n_cellsy): + for o in range(orientations): + centre = tuple([y * cy + cy // 2, x * cx + cx // 2]) + dx = radius * cos(float(o) / orientations * np.pi) + dy = radius * sin(float(o) / orientations * np.pi) + rr, cc = draw.bresenham(centre[0] - dx, centre[1] - dy, + centre[0] + dx, centre[1] + dy) + hog_image[rr, cc] += orientation_histogram[x, y, o] + + """ + The fourth stage computes normalisation, which takes local groups of + cells and contrast normalises their overall responses before passing + to next stage. Normalisation introduces better invariance to illumination, + shadowing, and edge contrast. It is performed by accumulating a measure + of local histogram "energy" over local groups of cells that we call + "blocks". The result is used to normalise each cell in the block. + Typically each individual cell is shared between several blocks, but + its normalisations are block dependent and thus different. The cell + thus appears several times in the final output vector with different + normalisations. This may seem redundant but it improves the performance. + We refer to the normalised block descriptors as Histogram of Oriented + Gradient (HOG) descriptors. + """ + + n_blocksx = (n_cellsx - bx) + 1 + n_blocksy = (n_cellsy - by) + 1 + normalised_blocks = np.zeros((n_blocksx, n_blocksy, + bx, by, orientations)) + + for x in range(n_blocksx): + for y in range(n_blocksy): + block = orientation_histogram[x:x + bx, y:y + by, :] + eps = 1e-5 + normalised_blocks[x, y, :] = block / sqrt(block.sum() ** 2 + eps) + + """ + The final step collects the HOG descriptors from all blocks of a dense + overlapping grid of blocks covering the detection window into a combined + feature vector for use in the window classifier. + """ + + if visualise: + return normalised_blocks.ravel(), hog_image + else: + return normalised_blocks.ravel() diff --git a/scikits/image/feature/tests/test_hog.py b/scikits/image/feature/tests/test_hog.py new file mode 100644 index 00000000..6f375cea --- /dev/null +++ b/scikits/image/feature/tests/test_hog.py @@ -0,0 +1,17 @@ +import numpy as np +import scipy + +from scikits.image.feature import hog + +def test_histogram_of_oriented_gradients(): + # Replace with scikits.image.data.lena() after merge + img = scipy.misc.lena().astype(np.int8) + + fd = hog(img, orientations=9, pixels_per_cell=(8, 8), + cells_per_block=(1, 1)) + + assert len(fd) == 9 * (512//8) ** 2 + +if __name__ == '__main__': + from numpy.testing import run_module_suite + run_module_suite() diff --git a/scikits/image/setup.py b/scikits/image/setup.py index 2a55b2b9..1e68ccec 100644 --- a/scikits/image/setup.py +++ b/scikits/image/setup.py @@ -14,6 +14,8 @@ def configuration(parent_package='', top_path=None): config.add_subpackage('data') config.add_subpackage('util') config.add_subpackage('color') + config.add_subpackage('draw') + config.add_subpackage('feature') def add_test_directories(arg, dirname, fnames): if dirname.split(os.path.sep)[-1] == 'tests':