import numpy as np
from . import _hoghistogram
from .._shared import utils
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=channel.dtype)
g_row[0, :] = 0
g_row[-1, :] = 0
g_row[1:-1, :] = channel[2:, :] - channel[:-2, :]
g_col = np.empty(channel.shape, dtype=channel.dtype)
g_col[:, 0] = 0
g_col[:, -1] = 0
g_col[:, 1:-1] = channel[:, 2:] - channel[:, :-2]
return g_row, g_col
[文档]
@utils.channel_as_last_axis(multichannel_output=False)
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,
*,
channel_axis=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.
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
`channel_axis` was added in 0.19.
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.
Raises
------
ValueError
If the image is too small given the values of pixels_per_cell and
cells_per_block.
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)
float_dtype = utils._supported_float_type(image.dtype)
image = image.astype(float_dtype, copy=False)
multichannel = channel_axis is not None
ndim_spatial = image.ndim - 1 if multichannel else image.ndim
if ndim_spatial != 2:
raise ValueError(
'Only images with two spatial dimensions are '
'supported. If using with color/multichannel '
'images, specify `channel_axis`.'
)
"""
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 multichannel:
g_row_by_ch = np.empty_like(image, dtype=float_dtype)
g_col_by_ch = np.empty_like(image, dtype=float_dtype)
g_magn = np.empty_like(image, dtype=float_dtype)
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), dtype=float
)
g_row = g_row.astype(float, copy=False)
g_col = g_col.astype(float, copy=False)
_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 + 0.5) / 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_dtype)
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
if n_blocks_col <= 0 or n_blocks_row <= 0:
min_row = b_row * c_row
min_col = b_col * c_col
raise ValueError(
'The input image is too small given the values of '
'pixels_per_cell and cells_per_block. '
'It should have at least: '
f'{min_row} rows and {min_col} cols.'
)
normalized_blocks = np.zeros(
(n_blocks_row, n_blocks_col, b_row, b_col, orientations), dtype=float_dtype
)
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
