ó  ‰\c @síddlmZddlZddlmZddlmZddlm Z ddl m Z ddl m Z dd lmZd d lmZdd lmZdd lmZd dlmZmZddlmZddd„Zd ddd„Zd dddd„Zd„Zd e d„Z!d„Z"d„Z#dddd„Z$d ddd„Z%ddd„Z&dddd d„Z'd d „Z(d d!„Z)d"d#d$„Z*d%d&d'„Z+d dd(e e ej,ddd)„Z-d d*„Z.d+„Z/dS(,iÿÿÿÿ(tcombinations_with_replacementN(tndimage(tstatsi(t img_as_float(tpeak_local_max(t_prepare_grayscale_input_2D(t _corner_fasti(t_hessian_matrix_det(tintegral_image(t safe_as_int(t_corner_moravect_corner_orientations(twarntconstanticCsLtj|ddd|d|ƒ}tj|ddd|d|ƒ}||fS(sCompute derivatives in x and y direction using the Sobel operator. Parameters ---------- image : ndarray Input image. mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. Returns ------- imx : ndarray Derivative in x-direction. imy : ndarray Derivative in y-direction. taxisitmodetcvali(tnditsobel(timageRRtimytimx((s5lib/python2.7/site-packages/skimage/feature/corner.pyt_compute_derivativess!!c Cst|ƒ}t|d|d|ƒ\}}tj|||d|d|ƒ}tj|||d|d|ƒ}tj|||d|d|ƒ}|||fS(sÑCompute structure tensor using sum of squared differences. The structure tensor A is defined as:: A = [Axx Axy] [Axy Ayy] which is approximated by the weighted sum of squared differences in a local window around each pixel in the image. Parameters ---------- image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as a weighting function for the local summation of squared differences. mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. Returns ------- Axx : ndarray Element of the structure tensor for each pixel in the input image. Axy : ndarray Element of the structure tensor for each pixel in the input image. Ayy : ndarray Element of the structure tensor for each pixel in the input image. Examples -------- >>> from skimage.feature import structure_tensor >>> square = np.zeros((5, 5)) >>> square[2, 2] = 1 >>> Axx, Axy, Ayy = structure_tensor(square, sigma=0.1) >>> Axx array([[ 0., 0., 0., 0., 0.], [ 0., 1., 0., 1., 0.], [ 0., 4., 0., 4., 0.], [ 0., 1., 0., 1., 0.], [ 0., 0., 0., 0., 0.]]) RR(RRRtgaussian_filter( RtsigmaRRRRtAxxtAxytAyy((s5lib/python2.7/site-packages/skimage/feature/corner.pytstructure_tensor.s 0 """c CsÜt|ƒ}tj|d|d|d|ƒ}|d krd|jdkr[tdƒd}qdd}ntj|ƒ}t|jƒ}|dkrt |ƒ}ngt |dƒD]%\}} tj||d| ƒ^q­} | S( sßCompute Hessian matrix. The Hessian matrix is defined as:: H = [Hrr Hrc] [Hrc Hcc] which is computed by convolving the image with the second derivatives of the Gaussian kernel in the respective x- and y-directions. Parameters ---------- image : ndarray Input image. sigma : float Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. order : {'xy', 'rc'}, optional This parameter allows for the use of reverse or forward order of the image axes in gradient computation. 'xy' indicates the usage of the last axis initially (Hxx, Hxy, Hyy), whilst 'rc' indicates the use of the first axis initially (Hrr, Hrc, Hcc). Returns ------- Hrr : ndarray Element of the Hessian matrix for each pixel in the input image. Hrc : ndarray Element of the Hessian matrix for each pixel in the input image. Hcc : ndarray Element of the Hessian matrix for each pixel in the input image. Examples -------- >>> from skimage.feature import hessian_matrix >>> square = np.zeros((5, 5)) >>> square[2, 2] = 4 >>> Hrr, Hrc, Hcc = hessian_matrix(square, sigma=0.1, order = 'rc') >>> Hrc array([[ 0., 0., 0., 0., 0.], [ 0., 1., 0., -1., 0.], [ 0., 0., 0., 0., 0.], [ 0., -1., 0., 1., 0.], [ 0., 0., 0., 0., 0.]]) RRRis¾deprecation warning: the default order of the hessian matrix values will be "row-column" instead of "xy" starting in skimage version 0.15. Use order="rc" or order="xy" to set this explicitlytxytrcRN( RRRtNonetndimR tnptgradienttrangetreversedR( RRRRtordertgaussian_filteredt gradientstaxestax0tax1tH_elems((s5lib/python2.7/site-packages/skimage/feature/corner.pythessian_matrixjs4      8cCs“|d}tj|j|j|jfƒ}x`ttt|jƒdƒƒD]@\}\}}|||d||f<|||d||f>> from skimage.feature import structure_tensor, structure_tensor_eigvals >>> square = np.zeros((5, 5)) >>> square[2, 2] = 1 >>> Axx, Axy, Ayy = structure_tensor(square, sigma=0.1) >>> structure_tensor_eigvals(Axx, Axy, Ayy)[0] array([[ 0., 0., 0., 0., 0.], [ 0., 2., 4., 2., 0.], [ 0., 4., 0., 4., 0.], [ 0., 2., 4., 2., 0.], [ 0., 0., 0., 0., 0.]]) (RB(RRR((s5lib/python2.7/site-packages/skimage/feature/corner.pytstructure_tensor_eigvalss"cCsÕ|dk r=|dkr!|}n|||g}tdƒnt|ƒdkrgtjt|Œƒ}njt|ƒ}tjj|ƒdddd…f}t t |j dƒƒ}tj ||j df|ƒ}|S(sÊCompute Eigenvalues of Hessian matrix. Parameters ---------- H_elems : list of ndarray The upper-diagonal elements of the Hessian matrix, as returned by `hessian_matrix`. Hxy : ndarray, deprecated Element of the Hessian matrix for each pixel in the input image. Hyy : ndarray, deprecated Element of the Hessian matrix for each pixel in the input image. Hxx : ndarray, deprecated Element of the Hessian matrix for each pixel in the input image. Returns ------- eigs : ndarray The eigenvalues of the Hessian matrix, in decreasing order. The eigenvalues are the leading dimension. That is, ``eigs[i, j, k]`` contains the ith-largest eigenvalue at position (j, k). Examples -------- >>> from skimage.feature import hessian_matrix, hessian_matrix_eigvals >>> square = np.zeros((5, 5)) >>> square[2, 2] = 4 >>> H_elems = hessian_matrix(square, sigma=0.1, order='rc') >>> hessian_matrix_eigvals(H_elems)[0] array([[ 0., 0., 2., 0., 0.], [ 0., 1., 0., 1., 0.], [ 2., 0., -2., 0., 2.], [ 0., 1., 0., 1., 0.], [ 0., 0., 2., 0., 0.]]) s¢The API of `hessian_matrix_eigvals` has changed. Use a list of elements instead of separate arguments. The old version of the API will be removed in version 0.16.i.Niÿÿÿÿi( RR tlenR!R5RBR4R6teigvalshttupleR#R t transpose(R+tHxytHyytHxxteigvalstmatricest leading_axes((s5lib/python2.7/site-packages/skimage/feature/corner.pythessian_matrix_eigvals+s#     % c CsZt|d|d|d|ddƒ}t|ƒ\}}dtjtj||||ƒS(suCompute the shape index. The shape index, as defined by Koenderink & van Doorn [1]_, is a single valued measure of local curvature, assuming the image as a 3D plane with intensities representing heights. It is derived from the eigen values of the Hessian, and its value ranges from -1 to 1 (and is undefined (=NaN) in *flat* regions), with following ranges representing following shapes: .. table:: Ranges of the shape index and corresponding shapes. =================== ============= Interval (s in ...) Shape =================== ============= [ -1, -7/8) Spherical cup [-7/8, -5/8) Through [-5/8, -3/8) Rut [-3/8, -1/8) Saddle rut [-1/8, +1/8) Saddle [+1/8, +3/8) Saddle ridge [+3/8, +5/8) Ridge [+5/8, +7/8) Dome [+7/8, +1] Spherical cap =================== ============= Parameters ---------- image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used for smoothing the input data before Hessian eigen value calculation. mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional How to handle values outside the image borders cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. Returns ------- s : ndarray Shape index References ---------- .. [1] Koenderink, J. J. & van Doorn, A. J., "Surface shape and curvature scales", Image and Vision Computing, 1992, 10, 557-564. DOI:10.1016/0262-8856(92)90076-F Examples -------- >>> from skimage.feature import shape_index >>> square = np.zeros((5, 5)) >>> square[2, 2] = 4 >>> s = shape_index(square, sigma=0.1) >>> s array([[ nan, nan, -0.5, nan, nan], [ nan, -0. , nan, -0. , nan], [-0.5, nan, -1. , nan, -0.5], [ nan, -0. , nan, -0. , nan], [ nan, nan, -0.5, nan, nan]]) RRRR%Rg@(R,RNR!tpitarctan(RRRRtHR@RA((s5lib/python2.7/site-packages/skimage/feature/corner.pyt shape_index`sB$c CsÔt|d|d|ƒ\}}t|d|d|ƒ\}}t|d|d|ƒ\}}||d||dd|||} |d|d} tj|dtjƒ} | dk} | | | | | | <| S(sÐCompute Kitchen and Rosenfeld corner measure response image. The corner measure is calculated as follows:: (imxx * imy**2 + imyy * imx**2 - 2 * imxy * imx * imy) / (imx**2 + imy**2) Where imx and imy are the first and imxx, imxy, imyy the second derivatives. Parameters ---------- image : ndarray Input image. mode : {'constant', 'reflect', 'wrap', 'nearest', 'mirror'}, optional How to handle values outside the image borders. cval : float, optional Used in conjunction with mode 'constant', the value outside the image boundaries. Returns ------- response : ndarray Kitchen and Rosenfeld response image. RRitdtypei(RR!t zeros_liketdouble( RRRRRtimxxtimxytimyxtimyyt numeratort denominatortresponsetmask((s5lib/python2.7/site-packages/skimage/feature/corner.pytcorner_kitchen_rosenfeld¨s* tkgš™™™™™©?gíµ ÷Æ°>c Cskt||ƒ\}}}|||d}||} |dkrU||| d} nd|| |} | S(sêCompute Harris corner measure response image. This corner detector uses information from the auto-correlation matrix A:: A = [(imx**2) (imx*imy)] = [Axx Axy] [(imx*imy) (imy**2)] [Axy Ayy] Where imx and imy are first derivatives, averaged with a gaussian filter. The corner measure is then defined as:: det(A) - k * trace(A)**2 or:: 2 * det(A) / (trace(A) + eps) Parameters ---------- image : ndarray Input image. method : {'k', 'eps'}, optional Method to compute the response image from the auto-correlation matrix. k : float, optional Sensitivity factor to separate corners from edges, typically in range `[0, 0.2]`. Small values of k result in detection of sharp corners. eps : float, optional Normalisation factor (Noble's corner measure). sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. Returns ------- response : ndarray Harris response image. References ---------- .. [1] http://kiwi.cs.dal.ca/~dparks/CornerDetection/harris.htm .. [2] http://en.wikipedia.org/wiki/Corner_detection Examples -------- >>> from skimage.feature import corner_harris, corner_peaks >>> square = np.zeros([10, 10]) >>> square[2:8, 2:8] = 1 >>> square.astype(int) array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) >>> corner_peaks(corner_harris(square), min_distance=1) array([[2, 2], [2, 7], [7, 2], [7, 7]]) iR_(R( RtmethodR_tepsRRRRtdetAttraceAR\((s5lib/python2.7/site-packages/skimage/feature/corner.pyt corner_harrisÓsB  cCsKt||ƒ\}}}||tj||dd|dƒd}|S(sœCompute Shi-Tomasi (Kanade-Tomasi) corner measure response image. This corner detector uses information from the auto-correlation matrix A:: A = [(imx**2) (imx*imy)] = [Axx Axy] [(imx*imy) (imy**2)] [Axy Ayy] Where imx and imy are first derivatives, averaged with a gaussian filter. The corner measure is then defined as the smaller eigenvalue of A:: ((Axx + Ayy) - sqrt((Axx - Ayy)**2 + 4 * Axy**2)) / 2 Parameters ---------- image : ndarray Input image. sigma : float, optional Standard deviation used for the Gaussian kernel, which is used as weighting function for the auto-correlation matrix. Returns ------- response : ndarray Shi-Tomasi response image. References ---------- .. [1] http://kiwi.cs.dal.ca/~dparks/CornerDetection/harris.htm .. [2] http://en.wikipedia.org/wiki/Corner_detection Examples -------- >>> from skimage.feature import corner_shi_tomasi, corner_peaks >>> square = np.zeros([10, 10]) >>> square[2:8, 2:8] = 1 >>> square.astype(int) array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) >>> corner_peaks(corner_shi_tomasi(square), min_distance=1) array([[2, 2], [2, 7], [7, 2], [7, 7]]) ii(RR!R<(RRRRRR\((s5lib/python2.7/site-packages/skimage/feature/corner.pytcorner_shi_tomasi$s7/c Cs®t||ƒ\}}}|||d}||}tj|dtjƒ}tj|dtjƒ}|dk} || || || >> from skimage.feature import corner_foerstner, corner_peaks >>> square = np.zeros([10, 10]) >>> square[2:8, 2:8] = 1 >>> square.astype(int) array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) >>> w, q = corner_foerstner(square) >>> accuracy_thresh = 0.5 >>> roundness_thresh = 0.3 >>> foerstner = (q > roundness_thresh) * (w > accuracy_thresh) * w >>> corner_peaks(foerstner, min_distance=1) array([[2, 2], [2, 7], [7, 2], [7, 7]]) iRSii(RR!RTRU( RRRRRRbRctwtqR]((s5lib/python2.7/site-packages/skimage/feature/corner.pytcorner_foerstnercs>  i g333333Ã?cCs1t|ƒ}tj|ƒ}t|||ƒ}|S(søExtract FAST corners for a given image. Parameters ---------- image : 2D ndarray Input image. n : int Minimum number of consecutive pixels out of 16 pixels on the circle that should all be either brighter or darker w.r.t testpixel. A point c on the circle is darker w.r.t test pixel p if `Ic < Ip - threshold` and brighter if `Ic > Ip + threshold`. Also stands for the n in `FAST-n` corner detector. threshold : float Threshold used in deciding whether the pixels on the circle are brighter, darker or similar w.r.t. the test pixel. Decrease the threshold when more corners are desired and vice-versa. Returns ------- response : ndarray FAST corner response image. References ---------- .. [1] Edward Rosten and Tom Drummond "Machine Learning for high-speed corner detection", http://www.edwardrosten.com/work/rosten_2006_machine.pdf .. [2] Wikipedia, "Features from accelerated segment test", https://en.wikipedia.org/wiki/Features_from_accelerated_segment_test Examples -------- >>> from skimage.feature import corner_fast, corner_peaks >>> square = np.zeros((12, 12)) >>> square[3:9, 3:9] = 1 >>> square.astype(int) array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) >>> corner_peaks(corner_fast(square, 9), min_distance=1) array([[3, 3], [3, 8], [8, 3], [8, 8]]) (RR!tascontiguousarrayR(Rtnt thresholdR\((s5lib/python2.7/site-packages/skimage/feature/corner.pyt corner_fast³s8 i g®Gáz®ï?c5Cs‘|dd}tj|d|ddddƒ}t||ƒ}tjd dtjƒ}tjd dtjƒ}tjddtjƒ}tjddtjƒ}|dd} tjjd|| | ƒ} tjj|| | ƒ} tj| |d…| |d…f\} } tj |dtjƒ}xXt |ƒD]J\}\}}||d}||d}||d}||d}|||…||…f}t |ddd dƒ\}}||dd …dd …f}||dd …dd …f}||dd …dd …f}tj |ƒ}tj |ƒ}tj |ƒ}tj || ƒ}tj || ƒ} tj || ƒ}!tj || ƒ}"tj || ƒ}#tj || ƒ}$||d<| |d<|d<||d<||d<||d<|d<||d<| |!|#|"f|(|$|!||"f|(y.tj j||ƒ}%tj j||ƒ}&Wn<tj jk r›tjtjf||d d …f>> from skimage.feature import corner_harris, corner_peaks, corner_subpix >>> img = np.zeros((10, 10)) >>> img[:5, :5] = 1 >>> img[5:, 5:] = 1 >>> img.astype(int) array([[1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1]]) >>> coords = corner_peaks(corner_harris(img), min_distance=2) >>> coords_subpix = corner_subpix(img, coords, window_size=7) >>> coords_subpix array([[ 4.5, 4.5]]) iit pad_widthRR tconstant_valuesiRSRiÿÿÿÿN(ii(ii(i(i(ii(ii(ii(ii(ii(ii(ii(ii(R!tpadR R-RURtftisftmgridRTR/RtsumR6tsolvet LinAlgErrortnantspacingtinftint(5Rtcornerst window_sizetalphatwexttN_dottN_edgetb_dottb_edget redundancyt t_crit_dott t_crit_edgetytxtcorners_subpixtity0tx0tminytmaxytminxtmaxxtwindowtwinxtwinyt winx_winxt winx_winyt winy_winyRRRtbxx_xtbxx_ytbxy_xtbxy_ytbyy_xtbyy_ytest_dottest_edgetry_dottrx_dottry_edgetrx_edgetrxx_dottrxy_dottryy_dottrxx_edgetrxy_edgetryy_edgetvar_dottvar_edgettt corner_class((s5lib/python2.7/site-packages/skimage/feature/corner.pyt corner_subpixòs’9!/       "      !!*    " / % 3 gš™™™™™¹?c Csõt|d|d|d|d|dtd|d|d|ƒ} |d krÎtj| jƒƒ} xn| D]c\} } | | | frdt| | || |d …| || |d …f>> from skimage.feature import peak_local_max >>> response = np.zeros((5, 5)) >>> response[2:4, 2:4] = 1 >>> response array([[ 0., 0., 0., 0., 0.], [ 0., 0., 0., 0., 0.], [ 0., 0., 1., 1., 0.], [ 0., 0., 1., 1., 0.], [ 0., 0., 0., 0., 0.]]) >>> peak_local_max(response) array([[3, 3], [3, 2], [2, 3], [2, 2]]) >>> corner_peaks(response) array([[2, 2]]) t min_distancet threshold_abst threshold_reltexclude_bordertindicest num_peakst footprinttlabelsiiN(RtFalseR!RGtnonzerotTrue( RR¬R­R®R¯R°R±R²R³tpeakstcoordstrtc((s5lib/python2.7/site-packages/skimage/feature/corner.pyt corner_peaks¡s"  4 cCs t||ƒS(sÕCompute Moravec corner measure response image. This is one of the simplest corner detectors and is comparatively fast but has several limitations (e.g. not rotation invariant). Parameters ---------- image : ndarray Input image. window_size : int, optional Window size. Returns ------- response : ndarray Moravec response image. References ---------- .. [1] http://kiwi.cs.dal.ca/~dparks/CornerDetection/moravec.htm .. [2] http://en.wikipedia.org/wiki/Corner_detection Examples -------- >>> from skimage.feature import corner_moravec >>> square = np.zeros([7, 7]) >>> square[3, 3] = 1 >>> square.astype(int) array([[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]) >>> corner_moravec(square).astype(int) array([[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 1, 2, 1, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]) (R (RR{((s5lib/python2.7/site-packages/skimage/feature/corner.pytcorner_moravec×s-cCst|||ƒS(s Compute the orientation of corners. The orientation of corners is computed using the first order central moment i.e. the center of mass approach. The corner orientation is the angle of the vector from the corner coordinate to the intensity centroid in the local neighborhood around the corner calculated using first order central moment. Parameters ---------- image : 2D array Input grayscale image. corners : (N, 2) array Corner coordinates as ``(row, col)``. mask : 2D array Mask defining the local neighborhood of the corner used for the calculation of the central moment. Returns ------- orientations : (N, 1) array Orientations of corners in the range [-pi, pi]. References ---------- .. [1] Ethan Rublee, Vincent Rabaud, Kurt Konolige and Gary Bradski "ORB : An efficient alternative to SIFT and SURF" http://www.vision.cs.chubu.ac.jp/CV-R/pdf/Rublee_iccv2011.pdf .. [2] Paul L. Rosin, "Measuring Corner Properties" http://users.cs.cf.ac.uk/Paul.Rosin/corner2.pdf Examples -------- >>> from skimage.morphology import octagon >>> from skimage.feature import (corner_fast, corner_peaks, ... corner_orientations) >>> square = np.zeros((12, 12)) >>> square[3:9, 3:9] = 1 >>> square.astype(int) array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) >>> corners = corner_peaks(corner_fast(square, 9), min_distance=1) >>> corners array([[3, 3], [3, 8], [8, 3], [8, 8]]) >>> orientations = corner_orientations(square, corners, octagon(3, 2)) >>> np.rad2deg(orientations) array([ 45., 135., -45., -135.]) (R (RRzR]((s5lib/python2.7/site-packages/skimage/feature/corner.pytcorner_orientationss?(0t itertoolsRtnumpyR!tscipyRRRtutilRtfeatureRt feature.utilRtfeature.corner_cyRt_hessian_det_appxRt transformRt _shared.utilsR t corner_cyR R twarningsR RRRR,R4R¶R;RBRCRNRRR^RdReRhRlR«RxR»R¼R½(((s5lib/python2.7/site-packages/skimage/feature/corner.pyts@ <Q -  %5H+Q ? 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