forked from 170010011/fr
180 lines
6.4 KiB
Python
180 lines
6.4 KiB
Python
import numpy as np
|
|
from scipy.signal import fftconvolve
|
|
|
|
from .._shared.utils import check_nD
|
|
|
|
|
|
def _window_sum_2d(image, window_shape):
|
|
|
|
window_sum = np.cumsum(image, axis=0)
|
|
window_sum = (window_sum[window_shape[0]:-1]
|
|
- window_sum[:-window_shape[0] - 1])
|
|
|
|
window_sum = np.cumsum(window_sum, axis=1)
|
|
window_sum = (window_sum[:, window_shape[1]:-1]
|
|
- window_sum[:, :-window_shape[1] - 1])
|
|
|
|
return window_sum
|
|
|
|
|
|
def _window_sum_3d(image, window_shape):
|
|
|
|
window_sum = _window_sum_2d(image, window_shape)
|
|
|
|
window_sum = np.cumsum(window_sum, axis=2)
|
|
window_sum = (window_sum[:, :, window_shape[2]:-1]
|
|
- window_sum[:, :, :-window_shape[2] - 1])
|
|
|
|
return window_sum
|
|
|
|
|
|
def match_template(image, template, pad_input=False, mode='constant',
|
|
constant_values=0):
|
|
"""Match a template to a 2-D or 3-D image using normalized correlation.
|
|
|
|
The output is an array with values between -1.0 and 1.0. The value at a
|
|
given position corresponds to the correlation coefficient between the image
|
|
and the template.
|
|
|
|
For `pad_input=True` matches correspond to the center and otherwise to the
|
|
top-left corner of the template. To find the best match you must search for
|
|
peaks in the response (output) image.
|
|
|
|
Parameters
|
|
----------
|
|
image : (M, N[, D]) array
|
|
2-D or 3-D input image.
|
|
template : (m, n[, d]) array
|
|
Template to locate. It must be `(m <= M, n <= N[, d <= D])`.
|
|
pad_input : bool
|
|
If True, pad `image` so that output is the same size as the image, and
|
|
output values correspond to the template center. Otherwise, the output
|
|
is an array with shape `(M - m + 1, N - n + 1)` for an `(M, N)` image
|
|
and an `(m, n)` template, and matches correspond to origin
|
|
(top-left corner) of the template.
|
|
mode : see `numpy.pad`, optional
|
|
Padding mode.
|
|
constant_values : see `numpy.pad`, optional
|
|
Constant values used in conjunction with ``mode='constant'``.
|
|
|
|
Returns
|
|
-------
|
|
output : array
|
|
Response image with correlation coefficients.
|
|
|
|
Notes
|
|
-----
|
|
Details on the cross-correlation are presented in [1]_. This implementation
|
|
uses FFT convolutions of the image and the template. Reference [2]_
|
|
presents similar derivations but the approximation presented in this
|
|
reference is not used in our implementation.
|
|
|
|
References
|
|
----------
|
|
.. [1] J. P. Lewis, "Fast Normalized Cross-Correlation", Industrial Light
|
|
and Magic.
|
|
.. [2] Briechle and Hanebeck, "Template Matching using Fast Normalized
|
|
Cross Correlation", Proceedings of the SPIE (2001).
|
|
:DOI:`10.1117/12.421129`
|
|
|
|
Examples
|
|
--------
|
|
>>> template = np.zeros((3, 3))
|
|
>>> template[1, 1] = 1
|
|
>>> template
|
|
array([[0., 0., 0.],
|
|
[0., 1., 0.],
|
|
[0., 0., 0.]])
|
|
>>> image = np.zeros((6, 6))
|
|
>>> image[1, 1] = 1
|
|
>>> image[4, 4] = -1
|
|
>>> image
|
|
array([[ 0., 0., 0., 0., 0., 0.],
|
|
[ 0., 1., 0., 0., 0., 0.],
|
|
[ 0., 0., 0., 0., 0., 0.],
|
|
[ 0., 0., 0., 0., 0., 0.],
|
|
[ 0., 0., 0., 0., -1., 0.],
|
|
[ 0., 0., 0., 0., 0., 0.]])
|
|
>>> result = match_template(image, template)
|
|
>>> np.round(result, 3)
|
|
array([[ 1. , -0.125, 0. , 0. ],
|
|
[-0.125, -0.125, 0. , 0. ],
|
|
[ 0. , 0. , 0.125, 0.125],
|
|
[ 0. , 0. , 0.125, -1. ]])
|
|
>>> result = match_template(image, template, pad_input=True)
|
|
>>> np.round(result, 3)
|
|
array([[-0.125, -0.125, -0.125, 0. , 0. , 0. ],
|
|
[-0.125, 1. , -0.125, 0. , 0. , 0. ],
|
|
[-0.125, -0.125, -0.125, 0. , 0. , 0. ],
|
|
[ 0. , 0. , 0. , 0.125, 0.125, 0.125],
|
|
[ 0. , 0. , 0. , 0.125, -1. , 0.125],
|
|
[ 0. , 0. , 0. , 0.125, 0.125, 0.125]])
|
|
"""
|
|
check_nD(image, (2, 3))
|
|
|
|
if image.ndim < template.ndim:
|
|
raise ValueError("Dimensionality of template must be less than or "
|
|
"equal to the dimensionality of image.")
|
|
if np.any(np.less(image.shape, template.shape)):
|
|
raise ValueError("Image must be larger than template.")
|
|
|
|
image_shape = image.shape
|
|
|
|
image = np.array(image, dtype=np.float64, copy=False)
|
|
|
|
pad_width = tuple((width, width) for width in template.shape)
|
|
if mode == 'constant':
|
|
image = np.pad(image, pad_width=pad_width, mode=mode,
|
|
constant_values=constant_values)
|
|
else:
|
|
image = np.pad(image, pad_width=pad_width, mode=mode)
|
|
|
|
# Use special case for 2-D images for much better performance in
|
|
# computation of integral images
|
|
if image.ndim == 2:
|
|
image_window_sum = _window_sum_2d(image, template.shape)
|
|
image_window_sum2 = _window_sum_2d(image ** 2, template.shape)
|
|
elif image.ndim == 3:
|
|
image_window_sum = _window_sum_3d(image, template.shape)
|
|
image_window_sum2 = _window_sum_3d(image ** 2, template.shape)
|
|
|
|
template_mean = template.mean()
|
|
template_volume = np.prod(template.shape)
|
|
template_ssd = np.sum((template - template_mean) ** 2)
|
|
|
|
if image.ndim == 2:
|
|
xcorr = fftconvolve(image, template[::-1, ::-1],
|
|
mode="valid")[1:-1, 1:-1]
|
|
elif image.ndim == 3:
|
|
xcorr = fftconvolve(image, template[::-1, ::-1, ::-1],
|
|
mode="valid")[1:-1, 1:-1, 1:-1]
|
|
|
|
numerator = xcorr - image_window_sum * template_mean
|
|
|
|
denominator = image_window_sum2
|
|
np.multiply(image_window_sum, image_window_sum, out=image_window_sum)
|
|
np.divide(image_window_sum, template_volume, out=image_window_sum)
|
|
denominator -= image_window_sum
|
|
denominator *= template_ssd
|
|
np.maximum(denominator, 0, out=denominator) # sqrt of negative number not allowed
|
|
np.sqrt(denominator, out=denominator)
|
|
|
|
response = np.zeros_like(xcorr, dtype=np.float64)
|
|
|
|
# avoid zero-division
|
|
mask = denominator > np.finfo(np.float64).eps
|
|
|
|
response[mask] = numerator[mask] / denominator[mask]
|
|
|
|
slices = []
|
|
for i in range(template.ndim):
|
|
if pad_input:
|
|
d0 = (template.shape[i] - 1) // 2
|
|
d1 = d0 + image_shape[i]
|
|
else:
|
|
d0 = template.shape[i] - 1
|
|
d1 = d0 + image_shape[i] - template.shape[i] + 1
|
|
slices.append(slice(d0, d1))
|
|
|
|
return response[tuple(slices)]
|