228 lines
7.9 KiB
Python
228 lines
7.9 KiB
Python
import numpy as np
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from scipy.interpolate import RectBivariateSpline
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from ..util import img_as_float
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from ..filters import sobel
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def active_contour(image, snake, alpha=0.01, beta=0.1,
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w_line=0, w_edge=1, gamma=0.01,
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max_px_move=1.0,
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max_iterations=2500, convergence=0.1,
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*,
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boundary_condition='periodic',
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coordinates='rc'):
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"""Active contour model.
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Active contours by fitting snakes to features of images. Supports single
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and multichannel 2D images. Snakes can be periodic (for segmentation) or
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have fixed and/or free ends.
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The output snake has the same length as the input boundary.
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As the number of points is constant, make sure that the initial snake
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has enough points to capture the details of the final contour.
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Parameters
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----------
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image : (N, M) or (N, M, 3) ndarray
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Input image.
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snake : (N, 2) ndarray
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Initial snake coordinates. For periodic boundary conditions, endpoints
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must not be duplicated.
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alpha : float, optional
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Snake length shape parameter. Higher values makes snake contract
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faster.
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beta : float, optional
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Snake smoothness shape parameter. Higher values makes snake smoother.
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w_line : float, optional
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Controls attraction to brightness. Use negative values to attract
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toward dark regions.
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w_edge : float, optional
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Controls attraction to edges. Use negative values to repel snake from
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edges.
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gamma : float, optional
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Explicit time stepping parameter.
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max_px_move : float, optional
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Maximum pixel distance to move per iteration.
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max_iterations : int, optional
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Maximum iterations to optimize snake shape.
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convergence : float, optional
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Convergence criteria.
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boundary_condition : string, optional
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Boundary conditions for the contour. Can be one of 'periodic',
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'free', 'fixed', 'free-fixed', or 'fixed-free'. 'periodic' attaches
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the two ends of the snake, 'fixed' holds the end-points in place,
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and 'free' allows free movement of the ends. 'fixed' and 'free' can
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be combined by parsing 'fixed-free', 'free-fixed'. Parsing
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'fixed-fixed' or 'free-free' yields same behaviour as 'fixed' and
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'free', respectively.
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coordinates : {'rc'}, optional
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This option remains for compatibility purpose only and has no effect.
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It was introduced in 0.16 with the ``'xy'`` option, but since 0.18,
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only the ``'rc'`` option is valid.
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Coordinates must be set in a row-column format.
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Returns
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-------
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snake : (N, 2) ndarray
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Optimised snake, same shape as input parameter.
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References
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----------
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.. [1] Kass, M.; Witkin, A.; Terzopoulos, D. "Snakes: Active contour
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models". International Journal of Computer Vision 1 (4): 321
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(1988). :DOI:`10.1007/BF00133570`
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Examples
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--------
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>>> from skimage.draw import circle_perimeter
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>>> from skimage.filters import gaussian
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Create and smooth image:
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>>> img = np.zeros((100, 100))
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>>> rr, cc = circle_perimeter(35, 45, 25)
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>>> img[rr, cc] = 1
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>>> img = gaussian(img, 2)
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Initialize spline:
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>>> s = np.linspace(0, 2*np.pi, 100)
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>>> init = 50 * np.array([np.sin(s), np.cos(s)]).T + 50
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Fit spline to image:
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>>> snake = active_contour(img, init, w_edge=0, w_line=1, coordinates='rc') # doctest: +SKIP
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>>> dist = np.sqrt((45-snake[:, 0])**2 + (35-snake[:, 1])**2) # doctest: +SKIP
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>>> int(np.mean(dist)) # doctest: +SKIP
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25
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"""
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if coordinates != 'rc':
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raise ValueError('Coordinate values must be set in a row column '
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'format. `coordinates` must be set to "rc".')
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max_iterations = int(max_iterations)
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if max_iterations <= 0:
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raise ValueError("max_iterations should be >0.")
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convergence_order = 10
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valid_bcs = ['periodic', 'free', 'fixed', 'free-fixed',
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'fixed-free', 'fixed-fixed', 'free-free']
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if boundary_condition not in valid_bcs:
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raise ValueError("Invalid boundary condition.\n" +
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"Should be one of: "+", ".join(valid_bcs)+'.')
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img = img_as_float(image)
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RGB = img.ndim == 3
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# Find edges using sobel:
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if w_edge != 0:
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if RGB:
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edge = [sobel(img[:, :, 0]), sobel(img[:, :, 1]),
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sobel(img[:, :, 2])]
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else:
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edge = [sobel(img)]
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else:
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edge = [0]
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# Superimpose intensity and edge images:
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if RGB:
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img = w_line*np.sum(img, axis=2) \
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+ w_edge*sum(edge)
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else:
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img = w_line*img + w_edge*edge[0]
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# Interpolate for smoothness:
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intp = RectBivariateSpline(np.arange(img.shape[1]),
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np.arange(img.shape[0]),
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img.T, kx=2, ky=2, s=0)
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snake_xy = snake[:, ::-1]
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x, y = snake_xy[:, 0].astype(float), snake_xy[:, 1].astype(float)
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n = len(x)
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xsave = np.empty((convergence_order, n))
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ysave = np.empty((convergence_order, n))
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# Build snake shape matrix for Euler equation
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a = np.roll(np.eye(n), -1, axis=0) + \
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np.roll(np.eye(n), -1, axis=1) - \
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2*np.eye(n) # second order derivative, central difference
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b = np.roll(np.eye(n), -2, axis=0) + \
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np.roll(np.eye(n), -2, axis=1) - \
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4*np.roll(np.eye(n), -1, axis=0) - \
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4*np.roll(np.eye(n), -1, axis=1) + \
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6*np.eye(n) # fourth order derivative, central difference
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A = -alpha*a + beta*b
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# Impose boundary conditions different from periodic:
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sfixed = False
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if boundary_condition.startswith('fixed'):
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A[0, :] = 0
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A[1, :] = 0
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A[1, :3] = [1, -2, 1]
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sfixed = True
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efixed = False
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if boundary_condition.endswith('fixed'):
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A[-1, :] = 0
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A[-2, :] = 0
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A[-2, -3:] = [1, -2, 1]
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efixed = True
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sfree = False
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if boundary_condition.startswith('free'):
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A[0, :] = 0
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A[0, :3] = [1, -2, 1]
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A[1, :] = 0
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A[1, :4] = [-1, 3, -3, 1]
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sfree = True
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efree = False
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if boundary_condition.endswith('free'):
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A[-1, :] = 0
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A[-1, -3:] = [1, -2, 1]
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A[-2, :] = 0
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A[-2, -4:] = [-1, 3, -3, 1]
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efree = True
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# Only one inversion is needed for implicit spline energy minimization:
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inv = np.linalg.inv(A + gamma*np.eye(n))
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# Explicit time stepping for image energy minimization:
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for i in range(max_iterations):
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fx = intp(x, y, dx=1, grid=False)
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fy = intp(x, y, dy=1, grid=False)
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if sfixed:
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fx[0] = 0
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fy[0] = 0
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if efixed:
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fx[-1] = 0
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fy[-1] = 0
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if sfree:
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fx[0] *= 2
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fy[0] *= 2
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if efree:
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fx[-1] *= 2
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fy[-1] *= 2
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xn = inv @ (gamma*x + fx)
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yn = inv @ (gamma*y + fy)
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# Movements are capped to max_px_move per iteration:
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dx = max_px_move*np.tanh(xn-x)
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dy = max_px_move*np.tanh(yn-y)
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if sfixed:
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dx[0] = 0
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dy[0] = 0
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if efixed:
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dx[-1] = 0
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dy[-1] = 0
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x += dx
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y += dy
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# Convergence criteria needs to compare to a number of previous
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# configurations since oscillations can occur.
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j = i % (convergence_order+1)
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if j < convergence_order:
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xsave[j, :] = x
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ysave[j, :] = y
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else:
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dist = np.min(np.max(np.abs(xsave-x[None, :]) +
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np.abs(ysave-y[None, :]), 1))
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if dist < convergence:
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break
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return np.stack([y, x], axis=1)
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