Fixed database typo and removed unnecessary class identifier.
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venv/Lib/site-packages/skimage/registration/_optical_flow.py
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venv/Lib/site-packages/skimage/registration/_optical_flow.py
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# coding: utf-8
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"""TV-L1 optical flow algorithm implementation.
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"""
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from functools import partial
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import numpy as np
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from scipy import ndimage as ndi
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from skimage.transform import warp
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from ._optical_flow_utils import coarse_to_fine
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def _tvl1(reference_image, moving_image, flow0, attachment, tightness,
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num_warp, num_iter, tol, prefilter):
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"""TV-L1 solver for optical flow estimation.
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Parameters
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----------
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reference_image : ndarray, shape (M, N[, P[, ...]])
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The first gray scale image of the sequence.
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moving_image : ndarray, shape (M, N[, P[, ...]])
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The second gray scale image of the sequence.
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flow0 : ndarray, shape (image0.ndim, M, N[, P[, ...]])
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Initialization for the vector field.
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attachment : float
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Attachment parameter. The smaller this parameter is,
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the smoother is the solutions.
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tightness : float
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Tightness parameter. It should have a small value in order to
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maintain attachement and regularization parts in
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correspondence.
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num_warp : int
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Number of times image1 is warped.
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num_iter : int
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Number of fixed point iteration.
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tol : float
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Tolerance used as stopping criterion based on the L² distance
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between two consecutive values of (u, v).
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prefilter : bool
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Whether to prefilter the estimated optical flow before each
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image warp.
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Returns
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-------
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flow : ndarray, shape ((image0.ndim, M, N[, P[, ...]])
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The estimated optical flow components for each axis.
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"""
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dtype = reference_image.dtype
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grid = np.meshgrid(*[np.arange(n, dtype=dtype)
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for n in reference_image.shape],
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indexing='ij')
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dt = 0.5 / reference_image.ndim
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reg_num_iter = 2
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f0 = attachment * tightness
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f1 = dt / tightness
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tol *= reference_image.size
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flow_current = flow_previous = flow0
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g = np.zeros((reference_image.ndim,) + reference_image.shape, dtype=dtype)
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proj = np.zeros((reference_image.ndim, reference_image.ndim,)
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+ reference_image.shape, dtype=dtype)
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s_g = [slice(None), ] * g.ndim
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s_p = [slice(None), ] * proj.ndim
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s_d = [slice(None), ] * (proj.ndim-2)
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for _ in range(num_warp):
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if prefilter:
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flow_current = ndi.median_filter(flow_current,
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[1] + reference_image.ndim * [3])
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image1_warp = warp(moving_image, grid + flow_current, mode='nearest')
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grad = np.array(np.gradient(image1_warp))
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NI = (grad*grad).sum(0)
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NI[NI == 0] = 1
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rho_0 = image1_warp - reference_image - (grad * flow_current).sum(0)
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for _ in range(num_iter):
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# Data term
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rho = rho_0 + (grad*flow_current).sum(0)
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idx = abs(rho) <= f0 * NI
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flow_auxiliary = flow_current
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flow_auxiliary[:, idx] -= rho[idx]*grad[:, idx]/NI[idx]
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idx = ~idx
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srho = f0 * np.sign(rho[idx])
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flow_auxiliary[:, idx] -= srho*grad[:, idx]
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# Regularization term
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flow_current = flow_auxiliary.copy()
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for idx in range(reference_image.ndim):
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s_p[0] = idx
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for _ in range(reg_num_iter):
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for ax in range(reference_image.ndim):
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s_g[0] = ax
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s_g[ax+1] = slice(0, -1)
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g[tuple(s_g)] = np.diff(flow_current[idx], axis=ax)
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s_g[ax+1] = slice(None)
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norm = np.sqrt((g ** 2).sum(0))[np.newaxis, ...]
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norm *= f1
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norm += 1.
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proj[idx] -= dt * g
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proj[idx] /= norm
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# d will be the (negative) divergence of proj[idx]
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d = -proj[idx].sum(0)
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for ax in range(reference_image.ndim):
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s_p[1] = ax
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s_p[ax+2] = slice(0, -1)
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s_d[ax] = slice(1, None)
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d[tuple(s_d)] += proj[tuple(s_p)]
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s_p[ax+2] = slice(None)
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s_d[ax] = slice(None)
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flow_current[idx] = flow_auxiliary[idx] + d
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flow_previous -= flow_current # The difference as stopping criteria
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if (flow_previous*flow_previous).sum() < tol:
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break
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flow_previous = flow_current
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return flow_current
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def optical_flow_tvl1(reference_image, moving_image,
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*,
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attachment=15, tightness=0.3, num_warp=5, num_iter=10,
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tol=1e-4, prefilter=False, dtype=np.float32):
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r"""Coarse to fine optical flow estimator.
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The TV-L1 solver is applied at each level of the image
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pyramid. TV-L1 is a popular algorithm for optical flow estimation
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introduced by Zack et al. [1]_, improved in [2]_ and detailed in [3]_.
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Parameters
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----------
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reference_image : ndarray, shape (M, N[, P[, ...]])
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The first gray scale image of the sequence.
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moving_image : ndarray, shape (M, N[, P[, ...]])
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The second gray scale image of the sequence.
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attachment : float, optional
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Attachment parameter (:math:`\lambda` in [1]_). The smaller
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this parameter is, the smoother the returned result will be.
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tightness : float, optional
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Tightness parameter (:math:`\tau` in [1]_). It should have
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a small value in order to maintain attachement and
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regularization parts in correspondence.
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num_warp : int, optional
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Number of times image1 is warped.
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num_iter : int, optional
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Number of fixed point iteration.
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tol : float, optional
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Tolerance used as stopping criterion based on the L² distance
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between two consecutive values of (u, v).
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prefilter : bool, optional
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Whether to prefilter the estimated optical flow before each
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image warp. This helps to remove the potential outliers.
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dtype : dtype, optional
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Output data type: must be floating point. Single precision
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provides good results and saves memory usage and computation
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time compared to double precision.
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Returns
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-------
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flow : ndarray, shape ((image0.ndim, M, N[, P[, ...]])
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The estimated optical flow components for each axis.
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Notes
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-----
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Color images are not supported.
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References
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----------
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.. [1] Zach, C., Pock, T., & Bischof, H. (2007, September). A
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duality based approach for realtime TV-L 1 optical flow. In Joint
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pattern recognition symposium (pp. 214-223). Springer, Berlin,
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Heidelberg. :DOI:`10.1007/978-3-540-74936-3_22`
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.. [2] Wedel, A., Pock, T., Zach, C., Bischof, H., & Cremers,
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D. (2009). An improved algorithm for TV-L 1 optical flow. In
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Statistical and geometrical approaches to visual motion analysis
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(pp. 23-45). Springer, Berlin, Heidelberg.
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:DOI:`10.1007/978-3-642-03061-1_2`
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.. [3] Pérez, J. S., Meinhardt-Llopis, E., & Facciolo,
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G. (2013). TV-L1 optical flow estimation. Image Processing On
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Line, 2013, 137-150. :DOI:`10.5201/ipol.2013.26`
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Examples
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--------
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>>> from skimage.color import rgb2gray
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>>> from skimage.data import stereo_motorcycle
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>>> from skimage.registration import optical_flow_tvl1
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>>> image0, image1, disp = stereo_motorcycle()
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>>> # --- Convert the images to gray level: color is not supported.
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>>> image0 = rgb2gray(image0)
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>>> image1 = rgb2gray(image1)
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>>> flow = optical_flow_tvl1(image1, image0)
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"""
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solver = partial(_tvl1, attachment=attachment,
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tightness=tightness, num_warp=num_warp, num_iter=num_iter,
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tol=tol, prefilter=prefilter)
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return coarse_to_fine(reference_image, moving_image, solver, dtype=dtype)
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