œ,j LSSKJr SSKrSSKJr SSKJrJrJ r "SS5r g))SelfN)distance_matrix)check_nD_deprecate_estimateFailedEstimationc\rSrSrSrSrSr\S5r\ S\ \ -4Sj5r Sr S rS r\S 5r\S 5rS rg)ThinPlateSplineTransform u Thin-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.from_estimate(src, dst) Appyling the transformation to `src` approximates `dst`: >>> np.round(tps(src), 4) # doctest: +FLOAT_CMP 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]]) The estimation can fail - for example, if all the input or output points are the same. If this happens, you will get a transform that is not "truthy" - meaning that ``bool(tform)`` is ``False``: >>> if tps: ... print("Estimation succeeded.") Estimation succeeded. Not so for a degenerate transform with identical points. >>> bad_src = np.ones((4, 2)) >>> bad_tps = ski.transform.ThinPlateSplineTransform.from_estimate( ... bad_src, dst) >>> if not bad_tps: ... print("Estimation failed.") Estimation failed. Trying to use this failed estimation transform result will give a suitable error: >>> bad_tps.params # doctest: +IGNORE_EXCEPTION_DETAIL Traceback (most recent call last): ... FailedEstimationAccessError: No attribute "params" for failed estimation ... c.SUlSUlSUlg)NF _estimated_spline_mappingssrcselfs ڳC:\Users\johnn\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\skimage/transform/_thin_plate_splines.py__init__!ThinPlateSplineTransform.__init__`s $c URc Sn[U5e[R"U5nURS:wdUR SS:wa Sn[U5eUR U5nURX5nU$)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__es  (% S/ !&! ;;! v||A!39CS/ !++F3 !226G!!rc[S5e)Nz Not supported)NotImplementedErrorrs rinverse ThinPlateSplineTransform.inverses !/22rreturncpU"5nURX5nUcU$[URSU35$)a Estimate 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 ------- tform : Self or ``FailedEstimation`` An instance of the transformation if the estimation succeeded. Otherwise, we return a special ``FailedEstimation`` object to signal a failed estimation. Testing the truth value of the failed estimation object will return ``False``. E.g. .. code-block:: python tform = ThinPlateSplineTransform.from_estimate(...) if not tform: raise RuntimeError(f"Failed estimation: {tf}") Notes ----- The number N of source and destination points must match. z: ) _estimater__name__)clsrdsttfr!s r from_estimate&ThinPlateSplineTransform.from_estimates=:Ull3$[rP&6#,,r#7O&PPrcl[USSS9 [USSS9 URSS:dURSS:a Sn[U5eURUR:wa'SURS UR3n[U5eXlURupE[ X5nUR U5n[ R"[ R"US 45U/5nUS-n [ R"X4[ RS 9n XzS U2S U24'XS U2S S 24'URU S S 2S U24'[ R"U[ R"US -U45/5n [ RRX5Ulg ![ RR a gf=f)z6Try to estimate and return reason if estimation fails.rr)arg_namer/rz,Need at least 3 points in in `src` and `dst`z'Shape of `src` and `dst` didn't match, z != r)dtypeNz#Unable to solve for spline mappings)rrrrr_radial_basis_kernelrhstackoneszerosfloat32Tvstacklinalgsolver LinAlgError) rrr/r!nddistKPn_plus_3LVs rr,"ThinPlateSplineTransform._estimatesa%(a%( 99Qrg)rwherelog)r_smallr_sqUs rr8-ThinPlateSplineTransform._radial_basis_kernels=!t HHQ#XsD266$-+@$@ Arc(URX5SL$)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. N)r,)rrr/s restimate!ThinPlateSplineTransform.estimates(~~c'4//rr N)r- __module__ __qualname____firstlineno____doc__rr$propertyr( classmethodrrr1r,rr staticmethodr8rr\__static_attributes__rrr r sTl "<33Q/?(?QQ@<0 "&00rr ) typingrnumpyr scipy.spatialr _shared.utilsrrrr rfrrrks )KKr0r0r