def estimate_alpha_lkm(image, trimap, laplacian_kwargs={}, cg_kwargs={}):
"""
Estimate alpha from an input image and an input trimap as described in Fast Matting Using Large Kernel Matting Laplacian Matrices by :cite:`he2010fast`.
Parameters
----------
image: numpy.ndarray
Image with shape :math:`h \\times w \\times d` for which the alpha matte should be estimated
trimap: numpy.ndarray
Trimap with shape :math:`h \\times w` of the image
laplacian_kwargs: dictionary
Arguments passed to the :code:`lkm_laplacian` function
cg_kwargs: dictionary
Arguments passed to the :code:`cg` solver
Returns
-------
alpha: numpy.ndarray
Estimated alpha matte
Example
-------
>>> from pymatting import *
>>> image = load_image("data/lemur/lemur.png", "RGB")
>>> trimap = load_image("data/lemur/lemur_trimap.png", "GRAY")
>>> alpha = estimate_alpha_lkm(
... image,
... trimap,
... laplacian_kwargs={"epsilon": 1e-6, "radius": 15},
... cg_kwargs={"maxiter":2000})
"""
sanity_check_image(image)
L_matvec, diag_L = lkm_laplacian(image, **laplacian_kwargs)
is_fg, is_bg, is_known, is_unknown = trimap_split(trimap)
lambda_value = 100.0
c = lambda_value * is_known
b = lambda_value * is_fg
inv_diag_A = 1.0 / (diag_L + c)
def A_matvec(x):
return L_matvec(x) + c * x
def jacobi(x):
return inv_diag_A * x
x = cg(A_matvec, b, M=jacobi, **cg_kwargs)
alpha = np.clip(x, 0, 1).reshape(trimap.shape)
return alpha
def estimate_alpha_lbdm(image,
trimap,
preconditioner=None,
laplacian_kwargs={},
cg_kwargs={}):
"""
Estimate alpha from an input image and an input trimap using Learning Based Digital Matting as proposed by :cite:`zheng2009learning`.
Parameters
----------
image: numpy.ndarray
Image with shape :math:`h \\times w \\times d` for which the alpha matte should be estimated
trimap: numpy.ndarray
Trimap with shape :math:`h \\times w` of the image
preconditioner: function or scipy.sparse.linalg.LinearOperator
Function or sparse matrix that applies the preconditioner to a vector (default: ichol)
laplacian_kwargs: dictionary
Arguments passed to the :code:`lbdm_laplacian` function
cg_kwargs: dictionary
Arguments passed to the :code:`cg` solver
Returns
-------
alpha: numpy.ndarray
Estimated alpha matte
Example
-------
>>> from pymatting import *
>>> image = load_image("data/lemur/lemur.png", "RGB")
>>> trimap = load_image("data/lemur/lemur_trimap.png", "GRAY")
>>> alpha = estimate_alpha_lbdm(
... image,
... trimap,
... laplacian_kwargs={"epsilon": 1e-6},
... cg_kwargs={"maxiter":2000})
"""
if preconditioner is None:
preconditioner = ichol
sanity_check_image(image)
A, b = make_linear_system(lbdm_laplacian(image, **laplacian_kwargs),
trimap)
x = cg(A, b, M=preconditioner(A), **cg_kwargs)
alpha = np.clip(x, 0, 1).reshape(trimap.shape)
return alpha
def estimate_alpha_knn(image,
trimap,
preconditioner=None,
laplacian_kwargs={},
cg_kwargs={}):
"""
Estimate alpha from an input image and an input trimap using KNN Matting similar to :cite:`chen2013knn`.
See `knn_laplacian` for more details.
Parameters
----------
image: numpy.ndarray
Image with shape :math:`h \\times w \\times d` for which the alpha matte should be estimated
trimap: numpy.ndarray
Trimap with shape :math:`h \\times w` of the image
preconditioner: function or scipy.sparse.linalg.LinearOperator
Function or sparse matrix that applies the preconditioner to a vector (default: jacobi)
laplacian_kwargs: dictionary
Arguments passed to the :code:`knn_laplacian` function
cg_kwargs: dictionary
Arguments passed to the :code:`cg` solver
Returns
-------
alpha: numpy.ndarray
Estimated alpha matte
Example
-------
>>> from pymatting import *
>>> image = load_image("data/lemur/lemur.png", "RGB")
>>> trimap = load_image("data/lemur/lemur_trimap.png", "GRAY")
>>> alpha = estimate_alpha_knn(
... image,
... trimap,
... laplacian_kwargs={"n_neighbors": [15, 10]},
... cg_kwargs={"maxiter":2000})
"""
if preconditioner is None:
preconditioner = jacobi
sanity_check_image(image)
A, b = make_linear_system(knn_laplacian(image, **laplacian_kwargs), trimap)
x = cg(A, b, M=preconditioner(A), **cg_kwargs)
alpha = np.clip(x, 0, 1).reshape(trimap.shape)
return alpha
def estimate_alpha_cf(image,
trimap,
preconditioner=None,
laplacian_kwargs={},
cg_kwargs={}):
"""
Estimate alpha from an input image and an input trimap using Closed-Form Alpha Matting as proposed by :cite:`levin2007closed`.
Parameters
----------
image: numpy.ndarray
Image with shape :math:`h \\times w \\times d` for which the alpha matte should be estimated
trimap: numpy.ndarray
Trimap with shape :math:`h \\times w` of the image
preconditioner: function or scipy.sparse.linalg.LinearOperator
Function or sparse matrix that applies the preconditioner to a vector (default: ichol)
laplacian_kwargs: dictionary
Arguments passed to the :code:`cf_laplacian` function
cg_kwargs: dictionary
Arguments passed to the :code:`cg` solver
is_known: numpy.ndarray
Binary mask of pixels for which to compute the laplacian matrix.
Providing this parameter might improve performance if few pixels are unknown.
Returns
-------
alpha: numpy.ndarray
Estimated alpha matte
Example
-------
>>> from pymatting import *
>>> image = load_image("data/lemur/lemur.png", "RGB")
>>> trimap = load_image("data/lemur/lemur_trimap.png", "GRAY")
>>> alpha = estimate_alpha_cf(
... image,
... trimap,
... laplacian_kwargs={"epsilon": 1e-6},
... cg_kwargs={"maxiter":2000})
"""
if preconditioner is None:
preconditioner = ichol
sanity_check_image(image)
h, w = trimap.shape[:2]
is_fg, is_bg, is_known, is_unknown = trimap_split(trimap)
L = cf_laplacian(image, **laplacian_kwargs, is_known=is_known)
# Split Laplacian matrix L into
#
# [L_U R ]
# [R^T L_K]
#
# and then solve L_U x_U = -R is_fg_K for x where K (is_known) corresponds to
# fixed pixels and U (is_unknown) corresponds to unknown pixels. For reference, see
# Grady, Leo, et al. "Random walks for interactive alpha-matting." Proceedings of VIIP. Vol. 2005. 2005.
L_U = L[is_unknown, :][:, is_unknown]
R = L[is_unknown, :][:, is_known]
m = is_fg[is_known]
x = trimap.copy().ravel()
x[is_unknown] = cg(L_U, -R.dot(m), M=preconditioner(L_U), **cg_kwargs)
alpha = np.clip(x, 0, 1).reshape(trimap.shape)
return alpha