def increment_mccf(A, B, X, y, nu=0.125, l=0.01, boundary='constant'):
r"""
Incremental Multi-Channel Correlation Filter (MCCF)
"""
# number of images; number of channels, height and width
n, k, hx, wx = X.shape
x_shape = (hx, wx)
# height and width of desired responses
_, hy, wy = y.shape
y_shape = (hy, wy)
# extended shape
ext_h = hx + hy - 1
ext_w = wx + wy - 1
ext_shape = (ext_h, ext_w)
# extended dimensionality
ext_d = ext_h * ext_w
# extend desired response
ext_y = pad(y, ext_shape)
# fft of extended desired response
fft_ext_y = fft2(ext_y)
# auto and cross spectral energy matrices
sXX = 0
sXY = 0
# for each training image and desired response
for x in X:
# extend image
ext_x = pad(x, ext_shape, boundary=boundary)
# fft of extended image
fft_ext_x = fft2(ext_x)
# store extended image fft as sparse diagonal matrix
diag_fft_x = spdiags(fft_ext_x.reshape((k, -1)),
-np.arange(0, k) * ext_d, ext_d * k, ext_d).T
# vectorize extended desired response fft
diag_fft_y = fft_ext_y.ravel()
# update auto and cross spectral energy matrices
sXX += diag_fft_x.conj().T.dot(diag_fft_x)
sXY += diag_fft_x.conj().T.dot(diag_fft_y)
# combine old and new auto and cross spectral energy matrices
sXY = (1 - nu) * A + nu * sXY
sXX = (1 - nu) * B + nu * sXX
# solve ext_d independent k x k linear systems (with regularization)
# to obtain desired extended multi-channel correlation filter
fft_ext_f = spsolve(sXX + l * speye(sXX.shape[-1]), sXY)
# reshape extended filter to extended image shape
fft_ext_f = fft_ext_f.reshape((k, ext_h, ext_w))
# compute filter inverse fft
ext_f = np.real(ifftshift(ifft2(fft_ext_f), axes=(-2, -1)))
# crop extended filter to match desired response shape
f = crop(ext_f, y_shape)
return f, sXY, sXX
def learn_kcf(x, y, kernel_correlation=gaussian_correlation, l=0.01,
boundary='constant', **kwargs):
r"""
Kernelized Correlation Filter (KCF).
Parameters
----------
x : ``(channels, height, width)`` `ndarray`
Template image.
y : ``(1, height, width)`` `ndarray`
Desired response.
kernel_correlation: `callable`, optional
Callable implementing a particular type of kernel correlation i.e.
gaussian, polynomial or linear.
l: `float`, optional
Regularization parameter.
boundary: str {`constant`, `symmetric`}, optional
Determines how the image is padded.
Returns
-------
alpha: ``(channels, height, width)`` `ndarray`
Kernelized Correlation Filter (KFC) associated to the template image.
References
----------
.. [1] J. F. Henriques, R. Caseiro, P. Martins, J. Batista. "High-Speed
Tracking with Kernelized Correlation Filters". TPAMI, 2015.
"""
# extended shape
x_shape = np.asarray(x.shape[-2:])
y_shape = np.asarray(y.shape[-2:])
ext_shape = x_shape + y_shape - 1
# extend desired response
ext_x = pad(x, ext_shape, boundary=boundary)
ext_y = pad(y, ext_shape)
# ffts of extended auto kernel correlation and extended desired response
fft_ext_kxx = fft2(kernel_correlation(ext_x, ext_x, **kwargs))
fft_ext_y = fft2(ext_y)
# extended kernelized correlation filter
ext_alpha = np.real(ifftshift(ifft2(fft_ext_y / (fft_ext_kxx + l)),
axes=(-2, -1)))
return crop(ext_alpha, y_shape), crop(x, y_shape)
def increment_mosse(A, B, X, y, nu=0.5, l=0.01, boundary='constant'):
r"""
Incremental Minimum Output Sum od Squared Errors (iMOSSE) filter
"""
# number of images, number of channels, height and width
n, k, hx, wx = X.shape
x_shape = (hx, wx)
# height and width of desired responses
_, hy, wy = y.shape
y_shape = (hy, wy)
# extended shape
ext_h = hx + hy - 1
ext_w = wx + wy - 1
ext_shape = (ext_h, ext_w)
# extend desired response
ext_y = pad(y, ext_shape)
# fft of extended desired response
fft_ext_y = fft2(ext_y)
# auto and cross spectral energy matrices
sXX = 0
sXY = 0
# for each training image and desired response
for x in X:
# extend image
ext_x = pad(x, ext_shape, boundary=boundary)
# fft of extended image
fft_ext_x = fft2(ext_x)
# update auto and cross spectral energy matrices
sXX += fft_ext_x.conj() * fft_ext_x
sXY += fft_ext_x.conj() * fft_ext_y
# combine old and new auto and cross spectral energy matrices
sXY = (1 - nu) * A + nu * sXY
sXX = (1 - nu) * B + nu * sXX
# compute desired correlation filter
fft_ext_f = sXY / (sXX + l)
# reshape extended filter to extended image shape
fft_ext_f = fft_ext_f.reshape((k, ext_h, ext_w))
# compute filter inverse fft
ext_f = np.real(ifftshift(ifft2(fft_ext_f), axes=(-2, -1)))
# crop extended filter to match desired response shape
f = crop(ext_f, y_shape)
return f, sXY, sXX
def learn_mosse(X, y, l=0.01, boundary='constant'):
r"""
Minimum Output Sum od Squared Errors (MOSSE) filter.
Parameters
----------
X : ``(n_images, n_channels, height, width)`` `ndarray`
Training images.
y : ``(1, height, width)`` `ndarray`
Desired response.
l: `float`, optional
Regularization parameter.
boundary: str {`constant`, `symmetric`}, optional
Determines how the image is padded.
Returns
-------
mosse: ``(1, height, width)`` `ndarray`
Minimum Output Sum od Squared Errors (MOSSE) filter associated to
the training images.
References
----------
.. [1] David S. Bolme, J. Ross Beveridge, Bruce A. Draper and Yui Man Lui.
"High-Speed Tracking with Kernelized Correlation Filters". CVPR, 2010.
"""
# number of images, number of channels, height and width
n, k, hx, wx = X.shape
# height and width of desired responses
_, hy, wy = y.shape
y_shape = (hy, wy)
# extended shape
ext_h = hx + hy - 1
ext_w = wx + wy - 1
ext_shape = (ext_h, ext_w)
# extend desired response
ext_y = pad(y, ext_shape)
# fft of extended desired response
fft_ext_y = fft2(ext_y)
# auto and cross spectral energy matrices
sXX = 0
sXY = 0
# for each training image and desired response
for x in X:
# extend image
ext_x = pad(x, ext_shape, boundary=boundary)
# fft of extended image
fft_ext_x = fft2(ext_x)
# update auto and cross spectral energy matrices
sXX += fft_ext_x.conj() * fft_ext_x
sXY += fft_ext_x.conj() * fft_ext_y
# compute desired correlation filter
fft_ext_f = sXY / (sXX + l)
# reshape extended filter to extended image shape
fft_ext_f = fft_ext_f.reshape((k, ext_h, ext_w))
# compute filter inverse fft
ext_f = np.real(ifftshift(ifft2(fft_ext_f), axes=(-2, -1)))
# crop extended filter to match desired response shape
f = crop(ext_f, y_shape)
return f, sXY, sXX
def learn_mccf(X, y, l=0.01, boundary='constant'):
r"""
Multi-Channel Correlation Filter (MCCF).
Parameters
----------
X : ``(n_images, n_channels, height, width)`` `ndarray`
Training images.
y : ``(1, height, width)`` `ndarray`
Desired response.
l: `float`, optional
Regularization parameter.
boundary: str {`constant`, `symmetric`}, optional
Determines how the image is padded.
Returns
-------
mccf: ``(1, height, width)`` `ndarray`
Multi-Channel Correlation Filter (MCCF) filter associated to the
training images.
References
----------
.. [1] Hamed Kiani Galoogahi, Terence Sim, Simon Lucey. "Multi-Channel
Correlation Filters". ICCV, 2013.
"""
# number of images; number of channels, height and width
n, k, hx, wx = X.shape
# height and width of desired responses
_, hy, wy = y.shape
y_shape = (hy, wy)
# extended shape
ext_h = hx + hy - 1
ext_w = wx + wy - 1
ext_shape = (ext_h, ext_w)
# extended dimensionality
ext_d = ext_h * ext_w
# extend desired response
ext_y = pad(y, ext_shape)
# fft of extended desired response
fft_ext_y = fft2(ext_y)
# auto and cross spectral energy matrices
sXX = 0
sXY = 0
# for each training image and desired response
for x in X:
# extend image
ext_x = pad(x, ext_shape, boundary=boundary)
# fft of extended image
fft_ext_x = fft2(ext_x)
# store extended image fft as sparse diagonal matrix
diag_fft_x = spdiags(fft_ext_x.reshape((k, -1)),
-np.arange(0, k) * ext_d, ext_d * k, ext_d).T
# vectorize extended desired response fft
diag_fft_y = fft_ext_y.ravel()
# update auto and cross spectral energy matrices
sXX += diag_fft_x.conj().T.dot(diag_fft_x)
sXY += diag_fft_x.conj().T.dot(diag_fft_y)
# solve ext_d independent k x k linear systems (with regularization)
# to obtain desired extended multi-channel correlation filter
fft_ext_f = spsolve(sXX + l * speye(sXX.shape[-1]), sXY)
# reshape extended filter to extended image shape
fft_ext_f = fft_ext_f.reshape((k, ext_h, ext_w))
# compute filter inverse fft
ext_f = np.real(ifftshift(ifft2(fft_ext_f), axes=(-2, -1)))
# crop extended filter to match desired response shape
f = crop(ext_f, y_shape)
return f, sXY, sXX
