h8SSKrSSKJr SSKJr "SS5rg)N)distance_matrix)check_nDcV\rSrSrSrSrSr\S5rSr Sr Sr \ S 5r S rg ) ThinPlateSplineTransformuThin-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]]) c.SUlSUlSUlg)NF _estimated_spline_mappingssrcselfs _/var/www/fran/franai/venv/lib/python3.13/site-packages/skimage/transform/_thin_plate_splines.py__init__!ThinPlateSplineTransform.__init__Gs $c URc Sn[U5e[R"U5nURS:wdUR SS:wa Sn[U5eUR U5nURX5nU$)zEstimate 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 zOTransformation is undefined, define it by calling `estimate` before applying itrz%Input `coords` must have shape (N, 2))r ValueErrornparrayndimshape_radial_distance_spline_function)rcoordsmsg radial_disttransformed_coordss r__call__!ThinPlateSplineTransform.__call__Ls  (% S/ !&! ;;! v||A!39CS/ !++F3 !226G!!rc[S5e)Nz Not supported)NotImplementedErrorrs rinverse ThinPlateSplineTransform.inversejs !/22rcl[USSS9 [USSS9 URSS:dURSS:a Sn[U5eURUR:wa'SURS UR3n[U5eXlURupE[ X5nUR U5n[ R"[ R"US 45U/5nUS-n [ R"X4[ RS 9n XzS U2S U24'XS U2S S 24'URU S S 2S U24'[ R"U[ R"US -U45/5n [ RRX5Ulg![ RR a gf=f)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 )arg_namedstrz,Need at least 3 points in in `src` and `dst`z'Shape of `src` and `dst` didn't match, z != r)dtypeNFT)rrrr r_radial_basis_kernelrhstackoneszerosfloat32Tvstacklinalgsolver LinAlgError) rr r)rnddistKPn_plus_3LVs restimate!ThinPlateSplineTransform.estimatens& a%(a%( 99Qrg)rwherelog)r_smallr_sqUs rr--ThinPlateSplineTransform._radial_basis_kernels=!t HHQ#XsD266$-+@$@ Arr N)__name__ __module__ __qualname____firstlineno____doc__rr!propertyr%r?rr staticmethodr-__static_attributes__rrrrsJ=~ "<33-^0 "rr)numpyr scipy.spatialr _shared.utilsrrrYrrr]s)$uur