import numpy as np from . import _hoghistogram def _hog_normalize_block(block, method, eps=1e-5): if method == 'L1': out = block / (np.sum(np.abs(block)) + eps) elif method == 'L1-sqrt': out = np.sqrt(block / (np.sum(np.abs(block)) + eps)) elif method == 'L2': out = block / np.sqrt(np.sum(block ** 2) + eps ** 2) elif method == 'L2-Hys': out = block / np.sqrt(np.sum(block ** 2) + eps ** 2) out = np.minimum(out, 0.2) out = out / np.sqrt(np.sum(out ** 2) + eps ** 2) else: raise ValueError('Selected block normalization method is invalid.') return out def _hog_channel_gradient(channel): """Compute unnormalized gradient image along `row` and `col` axes. Parameters ---------- channel : (M, N) ndarray Grayscale image or one of image channel. Returns ------- g_row, g_col : channel gradient along `row` and `col` axes correspondingly. """ g_row = np.empty(channel.shape, dtype=np.double) g_row[0, :] = 0 g_row[-1, :] = 0 g_row[1:-1, :] = channel[2:, :] - channel[:-2, :] g_col = np.empty(channel.shape, dtype=np.double) g_col[:, 0] = 0 g_col[:, -1] = 0 g_col[:, 1:-1] = channel[:, 2:] - channel[:, :-2] return g_row, g_col def hog(image, orientations=9, pixels_per_cell=(8, 8), cells_per_block=(3, 3), block_norm='L2-Hys', visualize=False, transform_sqrt=False, feature_vector=True, multichannel=None): """Extract Histogram of Oriented Gradients (HOG) for a given image. Compute a Histogram of Oriented Gradients (HOG) by 1. (optional) global image normalization 2. computing the gradient image in `row` and `col` 3. computing gradient histograms 4. normalizing across blocks 5. flattening into a feature vector Parameters ---------- image : (M, N[, C]) ndarray Input image. orientations : int, optional Number of orientation bins. pixels_per_cell : 2-tuple (int, int), optional Size (in pixels) of a cell. cells_per_block : 2-tuple (int, int), optional Number of cells in each block. block_norm : str {'L1', 'L1-sqrt', 'L2', 'L2-Hys'}, optional Block normalization method: ``L1`` Normalization using L1-norm. ``L1-sqrt`` Normalization using L1-norm, followed by square root. ``L2`` Normalization using L2-norm. ``L2-Hys`` Normalization using L2-norm, followed by limiting the maximum values to 0.2 (`Hys` stands for `hysteresis`) and renormalization using L2-norm. (default) For details, see [3]_, [4]_. visualize : bool, optional Also return an image of the HOG. For each cell and orientation bin, the image contains a line segment that is centered at the cell center, is perpendicular to the midpoint of the range of angles spanned by the orientation bin, and has intensity proportional to the corresponding histogram value. transform_sqrt : bool, optional Apply power law compression to normalize the image before processing. DO NOT use this if the image contains negative values. Also see `notes` section below. feature_vector : bool, optional Return the data as a feature vector by calling .ravel() on the result just before returning. multichannel : boolean, optional If True, the last `image` dimension is considered as a color channel, otherwise as spatial. Returns ------- out : (n_blocks_row, n_blocks_col, n_cells_row, n_cells_col, n_orient) ndarray HOG descriptor for the image. If `feature_vector` is True, a 1D (flattened) array is returned. hog_image : (M, N) ndarray, optional A visualisation of the HOG image. Only provided if `visualize` is True. References ---------- .. [1] https://en.wikipedia.org/wiki/Histogram_of_oriented_gradients .. [2] 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, https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf, :DOI:`10.1109/CVPR.2005.177` .. [3] Lowe, D.G., Distinctive image features from scale-invatiant keypoints, International Journal of Computer Vision (2004) 60: 91, http://www.cs.ubc.ca/~lowe/papers/ijcv04.pdf, :DOI:`10.1023/B:VISI.0000029664.99615.94` .. [4] Dalal, N, Finding People in Images and Videos, Human-Computer Interaction [cs.HC], Institut National Polytechnique de Grenoble - INPG, 2006, https://tel.archives-ouvertes.fr/tel-00390303/file/NavneetDalalThesis.pdf Notes ----- The presented code implements the HOG extraction method from [2]_ with the following changes: (I) blocks of (3, 3) cells are used ((2, 2) in the paper); (II) no smoothing within cells (Gaussian spatial window with sigma=8pix in the paper); (III) L1 block normalization is used (L2-Hys in the paper). Power law compression, also known as Gamma correction, is used to reduce the effects of shadowing and illumination variations. The compression makes the dark regions lighter. When the kwarg `transform_sqrt` is set to ``True``, the function computes the square root of each color channel and then applies the hog algorithm to the image. """ image = np.atleast_2d(image) if multichannel is None: multichannel = (image.ndim == 3) ndim_spatial = image.ndim - 1 if multichannel else image.ndim if ndim_spatial != 2: raise ValueError('Only images with 2 spatial dimensions are ' 'supported. If using with color/multichannel ' 'images, specify `multichannel=True`.') """ The first stage applies an optional global image normalization 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 color 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 transform_sqrt: image = np.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 color channel is used, which provides color 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. """ if image.dtype.kind == 'u': # convert uint image to float # to avoid problems with subtracting unsigned numbers image = image.astype('float') if multichannel: g_row_by_ch = np.empty_like(image, dtype=np.double) g_col_by_ch = np.empty_like(image, dtype=np.double) g_magn = np.empty_like(image, dtype=np.double) for idx_ch in range(image.shape[2]): g_row_by_ch[:, :, idx_ch], g_col_by_ch[:, :, idx_ch] = \ _hog_channel_gradient(image[:, :, idx_ch]) g_magn[:, :, idx_ch] = np.hypot(g_row_by_ch[:, :, idx_ch], g_col_by_ch[:, :, idx_ch]) # For each pixel select the channel with the highest gradient magnitude idcs_max = g_magn.argmax(axis=2) rr, cc = np.meshgrid(np.arange(image.shape[0]), np.arange(image.shape[1]), indexing='ij', sparse=True) g_row = g_row_by_ch[rr, cc, idcs_max] g_col = g_col_by_ch[rr, cc, idcs_max] else: g_row, g_col = _hog_channel_gradient(image) """ 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. """ s_row, s_col = image.shape[:2] c_row, c_col = pixels_per_cell b_row, b_col = cells_per_block n_cells_row = int(s_row // c_row) # number of cells along row-axis n_cells_col = int(s_col // c_col) # number of cells along col-axis # compute orientations integral images orientation_histogram = np.zeros((n_cells_row, n_cells_col, orientations)) _hoghistogram.hog_histograms(g_col, g_row, c_col, c_row, s_col, s_row, n_cells_col, n_cells_row, orientations, orientation_histogram) # now compute the histogram for each cell hog_image = None if visualize: from .. import draw radius = min(c_row, c_col) // 2 - 1 orientations_arr = np.arange(orientations) # set dr_arr, dc_arr to correspond to midpoints of orientation bins orientation_bin_midpoints = ( np.pi * (orientations_arr + .5) / orientations) dr_arr = radius * np.sin(orientation_bin_midpoints) dc_arr = radius * np.cos(orientation_bin_midpoints) hog_image = np.zeros((s_row, s_col), dtype=float) for r in range(n_cells_row): for c in range(n_cells_col): for o, dr, dc in zip(orientations_arr, dr_arr, dc_arr): centre = tuple([r * c_row + c_row // 2, c * c_col + c_col // 2]) rr, cc = draw.line(int(centre[0] - dc), int(centre[1] + dr), int(centre[0] + dc), int(centre[1] - dr)) hog_image[rr, cc] += orientation_histogram[r, c, o] """ The fourth stage computes normalization, which takes local groups of cells and contrast normalizes their overall responses before passing to next stage. Normalization 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 normalize each cell in the block. Typically each individual cell is shared between several blocks, but its normalizations are block dependent and thus different. The cell thus appears several times in the final output vector with different normalizations. This may seem redundant but it improves the performance. We refer to the normalized block descriptors as Histogram of Oriented Gradient (HOG) descriptors. """ n_blocks_row = (n_cells_row - b_row) + 1 n_blocks_col = (n_cells_col - b_col) + 1 normalized_blocks = np.zeros((n_blocks_row, n_blocks_col, b_row, b_col, orientations)) for r in range(n_blocks_row): for c in range(n_blocks_col): block = orientation_histogram[r:r + b_row, c:c + b_col, :] normalized_blocks[r, c, :] = \ _hog_normalize_block(block, method=block_norm) """ 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 feature_vector: normalized_blocks = normalized_blocks.ravel() if visualize: return normalized_blocks, hog_image else: return normalized_blocks