ó  ‰\c @s¼ddlZddlmZd„Zd„Zdd„Zdd„Zd„Z d „Z d „Z d „Z d „Z d „Zd„Zd„Zd„Zddddddded„ZdS(iÿÿÿÿN(tdistance_transform_edtc CsËtj|dddƒ}|dd…dd…f|dd…dd…fd}|dd…dd…f|dd…dd…fd}|dd…dd…f|dd…dd…fd|}|dd…dd…f|dd…dd…fd|}d |dd…dd…f|dd…dd…f|dd…dd…f|dd…dd…f}|d|d}||dd|||||d|tj|ƒd }|S( s2Returns the 'curvature' of a level set 'phi'. itmodetedgeiNiÿÿÿÿiþÿÿÿg@gÐ?g:Œ0âŽyE>(tnptpadtsqrt( tphitPtfytfxtfyytfxxtfxytgrad2tK((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt _cv_curvatures::>>n'cCsd}tj|dddƒ}|dd…dd…f|dd…dd…f}|dd…dd…f|dd…dd…f} |dd…dd…f|dd…dd…fd } |dd…dd…f|dd…dd…f} |dd…dd…f|dd…dd…f} |dd…dd…f|dd…dd…fd } d tj||d| dƒ}d tj|| d| dƒ}d tj|| d| dƒ}d tj|| d| dƒ}|dd…dd…f||dd…dd…f||dd…dd…f||dd…dd…f|}d|d k}t||ƒ\}}| ||d|||d}||t|ƒ|||}|d||t|ƒ||||S( sLReturns the variation of level set 'phi' based on algorithm parameters. g¼‰Ø—²Òœlib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_calculate_variations(66:66:####zgð?cCs$dddtjtj||ƒS(sVReturns the result of a regularised heavyside function of the input value(s). gà?gð?g@(Rtpitarctan(txteps((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt _cv_heavyside4scCs||d|dS(sRReturns the result of a regularised dirac function of the input value(s). i((R*R+((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyR;scCs|}d|}tj|ƒ}tj|ƒ}tj||ƒ}tj||ƒ}|dkrm||:}n|dkr†||:}n||fS(s7Returns the average values 'inside' and 'outside'. gð?i(Rtsum(RR"tHtHinvtHsumtHinvsumt avg_insidet avg_oustide((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyRBs     cCsGt||ƒ\}}d|}|||d||||d|S(svReturns the 'energy' contribution due to the difference from the average value within a region at each point. gð?i(R(RR"t lambda_post lambda_negR#R$R/((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt _cv_difference_from_average_termRs cCst|ƒ}||S(s„Returns the 'energy' contribution due to the length of the edge between regions at each point, multiplied by a factor 'mu'. (R(RRttoret((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_edge_length_term\s cCsJt|ƒ}t||||ƒ}t||ƒ}tj|ƒtj|ƒS(sBReturns the total 'energy' of the current level set function. (R,R6R8RR-(RRRRRR.t avgenergyt lenenergy((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt _cv_energyds cCs|S(sŒThis is a placeholder function as resetting the level set is not strictly necessary, and has not been done for this implementation. ((R((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_reset_level_setmscCsftj|dƒj|ddƒ}tj|dƒ}tjtj||ƒtjtj||ƒS(s„Generates a checkerboard level set function. According to Pascal Getreuer, such a level set function has fast convergence. ii(RtarangetreshapetsinR((t image_sizet square_sizetyvtxv((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_checkerboardts#cCsvtj|ƒ}t|dddƒ}t|dddƒ}d|||flib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_large_disks cCs~tj|ƒ}t|dddƒ}t|dddƒ}d|||flib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_small_diskŒs cCst|ƒtkru|dkr0t|dƒ}q{|dkrKt|ƒ}q{|dkrft|ƒ}q{tdƒ‚n|}|S(sLGenerates an initial level set function conditional on input arguments. t checkerboarditdisks small disks-Incorrect name for starting level set preset.(ttypetstrRDRNROt ValueError(tinit_level_sett image_shapeRJ((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt_cv_init_level_set™s   gÐ?gü©ñÒMbP?iôgà?RPc Cs©t|jƒdkr$tdƒ‚nt||jƒ} t| ƒtjks]| j|jkrltdƒ‚n|tj|ƒ}tj|ƒdkrª|tj|ƒ}nd} t || |||ƒ} g} |d} | dk}x§| |kr| |kr| }t || ||||ƒ} t | ƒ} tj | |dj ƒƒ} | dk}t || |||ƒ}| j| ƒ|} | d7} qçW|r¡|| | fS|SdS(sChan-Vese segmentation algorithm. Active contour model by evolving a level set. Can be used to segment objects without clearly defined boundaries. Parameters ---------- image : (M, N) ndarray Grayscale image to be segmented. mu : float, optional 'edge length' weight parameter. Higher `mu` values will produce a 'round' edge, while values closer to zero will detect smaller objects. lambda1 : float, optional 'difference from average' weight parameter for the output region with value 'True'. If it is lower than `lambda2`, this region will have a larger range of values than the other. lambda2 : float, optional 'difference from average' weight parameter for the output region with value 'False'. If it is lower than `lambda1`, this region will have a larger range of values than the other. tol : float, positive, optional Level set variation tolerance between iterations. If the L2 norm difference between the level sets of successive iterations normalized by the area of the image is below this value, the algorithm will assume that the solution was reached. max_iter : uint, optional Maximum number of iterations allowed before the algorithm interrupts itself. dt : float, optional A multiplication factor applied at calculations for each step, serves to accelerate the algorithm. While higher values may speed up the algorithm, they may also lead to convergence problems. init_level_set : str or (M, N) ndarray, optional Defines the starting level set used by the algorithm. If a string is inputted, a level set that matches the image size will automatically be generated. Alternatively, it is possible to define a custom level set, which should be an array of float values, with the same shape as 'image'. Accepted string values are as follows. 'checkerboard' the starting level set is defined as sin(x/5*pi)*sin(y/5*pi), where x and y are pixel coordinates. This level set has fast convergence, but may fail to detect implicit edges. 'disk' the starting level set is defined as the opposite of the distance from the center of the image minus half of the minimum value between image width and image height. This is somewhat slower, but is more likely to properly detect implicit edges. 'small disk' the starting level set is defined as the opposite of the distance from the center of the image minus a quarter of the minimum value between image width and image height. extended_output : bool, optional If set to True, the return value will be a tuple containing the three return values (see below). If set to False which is the default value, only the 'segmentation' array will be returned. Returns ------- segmentation : (M, N) ndarray, bool Segmentation produced by the algorithm. phi : (M, N) ndarray of floats Final level set computed by the algorithm. energies : list of floats Shows the evolution of the 'energy' for each step of the algorithm. This should allow to check whether the algorithm converged. Notes ----- The Chan-Vese Algorithm is designed to segment objects without clearly defined boundaries. This algorithm is based on level sets that are evolved iteratively to minimize an energy, which is defined by weighted values corresponding to the sum of differences intensity from the average value outside the segmented region, the sum of differences from the average value inside the segmented region, and a term which is dependent on the length of the boundary of the segmented region. This algorithm was first proposed by Tony Chan and Luminita Vese, in a publication entitled "An Active Countour Model Without Edges" [1]_. This implementation of the algorithm is somewhat simplified in the sense that the area factor 'nu' described in the original paper is not implemented, and is only suitable for grayscale images. Typical values for `lambda1` and `lambda2` are 1. If the 'background' is very different from the segmented object in terms of distribution (for example, a uniform black image with figures of varying intensity), then these values should be different from each other. Typical values for mu are between 0 and 1, though higher values can be used when dealing with shapes with very ill-defined contours. The 'energy' which this algorithm tries to minimize is defined as the sum of the differences from the average within the region squared and weighed by the 'lambda' factors to which is added the length of the contour multiplied by the 'mu' factor. Supports 2D grayscale images only, and does not implement the area term described in the original article. References ---------- .. [1] An Active Contour Model without Edges, Tony Chan and Luminita Vese, Scale-Space Theories in Computer Vision, 1999, DOI:10.1007/3-540-48236-9_13 .. [2] Chan-Vese Segmentation, Pascal Getreuer Image Processing On Line, 2 (2012), pp. 214-224, DOI:10.5201/ipol.2012.g-cv .. [3] The Chan-Vese Algorithm - Project Report, Rami Cohen, http://arxiv.org/abs/1107.2782, 2011 is!Input image should be a 2D array.sIThe dimensions of initial level set do not match the dimensions of image.iiN(tlentshapeRTRWRRRtndarrayRHtmaxR;R'R<Rtmeantappend(RRRRttoltmax_iterRRUtextended_outputRtit old_energytenergiestphivart segmentationtoldphit new_energy((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyt chan_veseªs4'      (tnumpyRt scipy.ndimageRRIRR'R,RRR6R8R;R<RDRNRORWtFalseRh(((s>lib/python2.7/site-packages/skimage/segmentation/_chan_vese.pyts"