o j@s2ddlZddlmZddlmZGdddZdS)N)distance_matrix)check_nDc@sPeZdZdZddZddZeddZdd Zd d Z d d Z e ddZ dS)ThinPlateSplineTransformulThin-plate spline transformation. Given two matching sets of points, source and destination, this class estimates the thin-plate spline (TPS) transformation which transforms each point in source into its destination counterpart. Attributes ---------- src : (N, 2) array_like Coordinates of control points in source image. References ---------- .. [1] Bookstein, Fred L. "Principal warps: Thin-plate splines and the decomposition of deformations," IEEE Transactions on pattern analysis and machine intelligence 11.6 (1989): 567–585. DOI:`10.1109/34.24792` https://user.engineering.uiowa.edu/~aip/papers/bookstein-89.pdf Examples -------- >>> import skimage as ski Define source and destination control points such that they simulate rotating by 90 degrees and generate a meshgrid from them: >>> src = np.array([[0, 0], [0, 5], [5, 5], [5, 0]]) >>> dst = np.array([[5, 0], [0, 0], [0, 5], [5, 5]]) Estimate the transformation: >>> tps = ski.transform.ThinPlateSplineTransform() >>> tps.estimate(src, dst) True Appyling the transformation to `src` approximates `dst`: >>> np.round(tps(src)) array([[5., 0.], [0., 0.], [0., 5.], [5., 5.]]) Create a meshgrid to apply the transformation to: >>> grid = np.meshgrid(np.arange(5), np.arange(5)) >>> grid[1] array([[0, 0, 0, 0, 0], [1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [3, 3, 3, 3, 3], [4, 4, 4, 4, 4]]) >>> coords = np.vstack([grid[0].ravel(), grid[1].ravel()]).T >>> transformed = tps(coords) >>> np.round(transformed[:, 1]).reshape(5, 5).astype(int) array([[0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4]]) cCsd|_d|_d|_dS)NF)Z _estimated_spline_mappingssrcselfr f/var/www/html/Deteccion_Ine/venv/lib/python3.10/site-packages/skimage/transform/_thin_plate_splines.py__init__Gs z!ThinPlateSplineTransform.__init__cCs^|jdur d}t|t|}|jdks|jddkr"d}t|||}|||}|S)a*Estimate the transformation from a set of corresponding points. Parameters ---------- coords : (N, 2) array_like x, y coordinates to transform Returns ------- transformed_coords: (N, D) array Destination coordinates NzOTransformation is undefined, define it by calling `estimate` before applying itrz%Input `coords` must have shape (N, 2))r ValueErrornparrayndimshape_radial_distance_spline_function)r coordsmsg radial_disttransformed_coordsr r r __call__Ls    z!ThinPlateSplineTransform.__call__cCstd)Nz Not supported)NotImplementedErrorrr r r inversejsz ThinPlateSplineTransform.inversec CsNt|dddt|ddd|jddks|jddkr"d}t||j|jkr6d|jd |j}t|||_|j\}}t||}||}tt|d f|g}|d} tj | | ftj d } || d |d |f<|| d |d d f<|j | d d d |f<t |t |d |fg} z tj | | |_WdStj jyYdSw)aEstimate optimal spline mappings between source and destination points. Parameters ---------- src : (N, 2) array_like Control points at source coordinates. dst : (N, 2) array_like Control points at destination coordinates. Returns ------- success: bool True indicates that the estimation was successful. Notes ----- The number N of source and destination points must match. rr)Zarg_namedstrz,Need at least 3 points in in `src` and `dst`z'Shape of `src` and `dst` didn't match, z != r )ZdtypeNFT)rrrrr_radial_basis_kernelrZhstackZonesZzerosZfloat32TZvstackZlinalgZsolverZ LinAlgError) r rrrnddistKPZn_plus_3LVr r r estimatens2    z!ThinPlateSplineTransform.estimatecCst||j}||S)zCCompute the radial distance between input points and source points.)rrr)r rdistsr r r rs  z)ThinPlateSplineTransform._radial_distancecCsT|jjd}|jd|}|j|d}|dt||ddt||}|S)z3Estimate the spline function in X and Y directions.rNr )rrrrdot)r rrr!warr r r rs (z)ThinPlateSplineTransform._spline_functionc Cs0d}|d}t|dkd|t||}|S)ajCompute the radial basis function for thin-plate splines. Parameters ---------- r : (4, N) ndarray Input array representing the Euclidean distance between each pair of two collections of control points. Returns ------- U : (4, N) ndarray Calculated kernel function U. g:0yE>rg)rwherelog)rZ_smallZr_sqUr r r rs z-ThinPlateSplineTransform._radial_basis_kernelN) __name__ __module__ __qualname____doc__r rpropertyrr(rr staticmethodrr r r r rs? /r)numpyrZ scipy.spatialrZ _shared.utilsrrr r r r s