ó  ‰\c@ sƒddlmZddlZddlZddlmZddlmZm Z d„Z d„Z d„Z d e fd „ƒYZd efd „ƒYZd efd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZied6ed6ed6ed6ed6ed 6ed!6ed"6Zd#„Zd$„ZdS(%iÿÿÿÿ(tdivisionN(tspatiali(tget_bound_method_classt safe_as_intcC s8tddddddƒ}||kr4||}n|S(sEConvert from `numpy.pad` mode name to the corresponding ndimage mode.tedgetnearestt symmetrictreflecttmirror(tdict(tmodetmode_translation_dict((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyt_to_ndimage_mode s    cC sStj|ddƒ}tjtj||dƒ|jdƒ}tjdƒ|}tj|d| |dgd|| |dgdddggƒ}tj|jtj |jdƒgƒ}tj ||ƒj}|dd…dd…f}|dd…dfc|dd…df<|dd…dfc|dd…df<||fS(sëCenter and normalize image points. The points are transformed in a two-step procedure that is expressed as a transformation matrix. The matrix of the resulting points is usually better conditioned than the matrix of the original points. Center the image points, such that the new coordinate system has its origin at the centroid of the image points. Normalize the image points, such that the mean distance from the points to the origin of the coordinate system is sqrt(2). Parameters ---------- points : (N, 2) array The coordinates of the image points. Returns ------- matrix : (3, 3) array The transformation matrix to obtain the new points. new_points : (N, 2) array The transformed image points. References ---------- .. [1] Hartley, Richard I. "In defense of the eight-point algorithm." Pattern Analysis and Machine Intelligence, IEEE Transactions on 19.6 (1997): 580-593. taxisiiiN( tnptmeantmathtsqrttsumtshapetarrayt row_stacktTtonestdot(tpointstcentroidtrmst norm_factortmatrixtpointsht new_pointsht new_points((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyt_center_and_normalize_pointss!+(,,cC s½|jd}|jd}|jddƒ}|jddƒ}||}||}tj|j|ƒ|} tj|fdtjƒ} tjj| ƒdkr¯d| |d“s    tFundamentalMatrixTransformcB sGeZdZdd„Zd„Zd„Zd„Zd„Zd„Z RS(sÑFundamental matrix transformation. The fundamental matrix relates corresponding points between a pair of uncalibrated images. The matrix transforms homogeneous image points in one image to epipolar lines in the other image. The fundamental matrix is only defined for a pair of moving images. In the case of pure rotation or planar scenes, the homography describes the geometric relation between two images (`ProjectiveTransform`). If the intrinsic calibration of the images is known, the essential matrix describes the metric relation between the two images (`EssentialMatrixTransform`). References ---------- .. [1] Hartley, Richard, and Andrew Zisserman. Multiple view geometry in computer vision. Cambridge university press, 2003. Parameters ---------- matrix : (3, 3) array, optional Fundamental matrix. Attributes ---------- params : (3, 3) array Fundamental matrix. cC sI|dkrtjdƒ}n|jdkr<tdƒ‚n||_dS(Nis&Invalid shape of transformation matrix(ii(tNoneRR&Rt ValueErrortparams(R@R((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyt__init__ñs  cC s;tj|tj|jdƒgƒ}tj||jjƒS(sApply forward transformation. Parameters ---------- coords : (N, 2) array Source coordinates. Returns ------- coords : (N, 3) array Epipolar lines in the destination image. i(Rt column_stackRRRRMR(R@RAtcoords_homogeneous((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRBùs%cC s8tj|tj|jdƒgƒ}tj||jƒS(sApply inverse transformation. Parameters ---------- coords : (N, 2) array Destination coordinates. Returns ------- coords : (N, 3) array Epipolar lines in the source image. i(RRORRRRM(R@RARP((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRC s%c C sÆ|j|jkst‚|jddks1t‚y(t|ƒ\}}t|ƒ\}}Wn@tk r›tjd tjƒ|_dtjd tjƒgSXtj|jddfƒ}||dd…dd…f<|dd…dd…fc|dd…dtj f9<||dd…dd…f<|dd…dd…fc|dd…d tj f9<||dd…dd…fs*Rotation matrix must have unit determinants#Invalid shape of translation vectors(Translation vector must have unit lengthiis&Invalid shape of transformation matrix(ii(ii(RKRLRR^RR$R%tsizetnormRRURRMR&(R@trotationt translationRtt_x((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRN±s(  ""'  c C s·|j||ƒ\}}}tjj|ƒ\}}}|d|dd|d<|d|dõssZYou cannot specify the transformation matrix and the implicit parameters at the same time.is'Invalid shape of transformation matrix.iii(ii(ii(ii( tanyRKRLRRMRRRtcostsinR&( R@RR<RgtshearRhRMtsxtsy((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRNós0            +*cC s\tj|jdd|jddƒ}tj|jdd|jddƒ}||fS(Niii(ii(ii(ii(ii(RRRM(R@R“R”((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR<s))cC stj|jd|jdƒS(Nii(ii(ii(Rtatan2RM(R@((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRgscC s,tj|jd |jdƒ}||jS(Nii(ii(ii(RR•RMRg(R@tbeta((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR’s!cC s|jdd…dfS(Nii(RM(R@((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRh#sN( RGRHRIRŠR{RKRNR‹R<RgR’Rh(((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRŒËs$   tPiecewiseAffineTransformcB s2eZdZd„Zd„Zd„Zd„ZRS(sõ2D piecewise affine transformation. Control points are used to define the mapping. The transform is based on a Delaunay triangulation of the points to form a mesh. Each triangle is used to find a local affine transform. Attributes ---------- affines : list of AffineTransform objects Affine transformations for each triangle in the mesh. inverse_affines : list of AffineTransform objects Inverse affine transformations for each triangle in the mesh. cC s(d|_d|_d|_d|_dS(N(RKt _tesselationt_inverse_tesselationtaffinestinverse_affines(R@((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRN8s   cC sútj|ƒ|_g|_x]|jjD]O}tƒ}|j||dd…f||dd…fƒ|jj|ƒq(Wtj|ƒ|_g|_ x]|jjD]O}tƒ}|j||dd…f||dd…fƒ|j j|ƒq£Wt S(s•Estimate the transformation from a set of corresponding points. Number of source and destination coordinates must match. Parameters ---------- src : (N, 2) array Source coordinates. dst : (N, 2) array Destination coordinates. Returns ------- success : bool True, if model estimation succeeds. N( RtDelaunayR˜RštverticesRŒR]tappendR™R›R[(R@R,R-ttritaffine((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR]>s  0  0cC s¯tj|tjƒ}|jj|ƒ}d||dkdd…fÔssZYou cannot specify the transformation matrix and the implicit parameters at the same time.is'Invalid shape of transformation matrix.iii(ii(ii( RRKRLRRMRRRRR‘R&(R@RRgRhRM((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRNÓs&       cC st||tƒ|_tS(sEstimate the transformation from a set of corresponding points. You can determine the over-, well- and under-determined parameters with the total least-squares method. Number of source and destination coordinates must match. Parameters ---------- src : (N, 2) array Source coordinates. dst : (N, 2) array Destination coordinates. Returns ------- success : bool True, if model estimation succeeds. (R=RqRMR[(R@R,R-((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR]îscC stj|jd|jdƒS(Nii(ii(ii(RR•RM(R@((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRgscC s|jdd…dfS(Nii(RM(R@((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRh sN( RGRHRIRKRNR]R‹RgRh(((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR¨®s # tSimilarityTransformcB s;eZdZddddd„Zd„Zed„ƒZRS(s 2D similarity transformation. Has the following form:: X = a0 * x - b0 * y + a1 = = s * x * cos(rotation) - s * y * sin(rotation) + a1 Y = b0 * x + a0 * y + b1 = = s * x * sin(rotation) + s * y * cos(rotation) + b1 where ``s`` is a scale factor and the homogeneous transformation matrix is:: [[a0 b0 a1] [b0 a0 b1] [0 0 1]] The similarity transformation extends the Euclidean transformation with a single scaling factor in addition to the rotation and translation parameters. Parameters ---------- matrix : (3, 3) array, optional Homogeneous transformation matrix. scale : float, optional Scale factor. rotation : float, optional Rotation angle in counter-clockwise direction as radians. translation : (tx, ty) as array, list or tuple, optional x, y translation parameters. Attributes ---------- params : (3, 3) array Homogeneous transformation matrix. cC smtd„|||fDƒƒ}|r@|dk r@tdƒ‚n)|dk rv|jdkrjtdƒ‚n||_nó|rW|dkr‘d}n|dkr¦d}n|dkr»d }ntjtj|ƒtj |ƒ dgtj |ƒtj|ƒdgdddggƒ|_|jdd…dd…fc|9<||jdd…df:ssZYou cannot specify the transformation matrix and the implicit parameters at the same time.is'Invalid shape of transformation matrix.iii(ii(ii( RRKRLRRMRRRRR‘R&(R@RR<RgRhRM((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRN8s,         %cC st||tƒ|_tS(sEstimate the transformation from a set of corresponding points. You can determine the over-, well- and under-determined parameters with the total least-squares method. Number of source and destination coordinates must match. Parameters ---------- src : (N, 2) array Source coordinates. dst : (N, 2) array Destination coordinates. Returns ------- success : bool True, if model estimation succeeds. (R=R[RM(R@R,R-((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR]WscC sXttj|jƒƒtjdƒkr7|jd}n|jdtj|jƒ}|S(Nii(ii(ii(R^RRRgRtspacingRM(R@R<((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR<qs'N(RGRHRIRKRNR]R‹R<(((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyR©s %   tPolynomialTransformcB s8eZdZdd„Zdd„Zd„Zd„ZRS(sp2D polynomial transformation. Has the following form:: X = sum[j=0:order]( sum[i=0:j]( a_ji * x**(j - i) * y**i )) Y = sum[j=0:order]( sum[i=0:j]( b_ji * x**(j - i) * y**i )) Parameters ---------- params : (2, N) array, optional Polynomial coefficients where `N * 2 = (order + 1) * (order + 2)`. So, a_ji is defined in `params[0, :]` and b_ji in `params[1, :]`. Attributes ---------- params : (2, N) array Polynomial coefficients where `N * 2 = (order + 1) * (order + 2)`. So, a_ji is defined in `params[0, :]` and b_ji in `params[1, :]`. cC se|dkr6tjdddgdddggƒ}n|jddkrXtdƒ‚n||_dS(Niiis*invalid shape of transformation parameters(RKRRRRLRM(R@RM((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyRN‘s  *icC sÀ|dd…df}|dd…df}|dd…df}|dd…df}|jd}t|ƒ}|d|d} tj|d| dfƒ} d} x‘t|dƒD]} xvt| dƒD]d} || | || | d|…| f<|| | || | |d…| | df<| d7} qÎWq·W|| d|…df<|| |d…df>> import numpy as np >>> from skimage import transform as tf >>> # estimate transformation parameters >>> src = np.array([0, 0, 10, 10]).reshape((2, 2)) >>> dst = np.array([12, 14, 1, -20]).reshape((2, 2)) >>> tform = tf.estimate_transform('similarity', src, dst) >>> np.allclose(tform.inverse(tform(src)), src) True >>> # warp image using the estimated transformation >>> from skimage import data >>> image = data.camera() >>> warp(image, inverse_map=tform.inverse) # doctest: +SKIP >>> # create transformation with explicit parameters >>> tform2 = tf.SimilarityTransform(scale=1.1, rotation=1, ... translation=(10, 20)) >>> # unite transformations, applied in order from left to right >>> tform3 = tform + tform2 >>> np.allclose(tform3(src), tform2(tform(src))) True s.the transformation type '%s' is notimplemented(tlowert TRANSFORMSRLR](tttypeR,R-tkwargsR‰((s;lib/python2.7/site-packages/skimage/transform/_geometric.pytestimate_transforms?    cC st|ƒ|ƒS(sApply 2D matrix transform. Parameters ---------- coords : (N, 2) array x, y coordinates to transform matrix : (3, 3) array Homogeneous transformation matrix. Returns ------- coords : (N, 2) array Transformed coordinates. (Rl(RAR((s;lib/python2.7/site-packages/skimage/transform/_geometric.pytmatrix_transformes(t __future__RRtnumpyRtscipyRt _shared.utilsRRR R!R=tobjectR>RJRdRlRŒR—R¨R©R«R»R¾R¿(((s;lib/python2.7/site-packages/skimage/transform/_geometric.pyts6   6 K@ºbÜ]†cj”  J