o :ήc?K @sdZddlmZddlZddlmZmZddlm Z m Z ddl m Z m Z d!d d Zd"d d Zd dZ  d#ddZedddddddfddZeddddddfddZedddddddddddf ddZedddddddddddf dd ZdS)$ab Ridge filters. Ridge filters can be used to detect continuous edges, such as vessels, neurites, wrinkles, rivers, and other tube-like structures. The present class of ridge filters relies on the eigenvalues of the Hessian matrix of image intensities to detect tube-like structures where the intensity changes perpendicular but not along the structure. )warnN)_supported_float_typecheck_nD)hessian_matrixhessian_matrix_eigvals) img_as_floatinvert绽|=cCs"t|}|||dk<t||S)a Divides two arrays. Denominator is set to small value where zero to avoid ZeroDivisionError and return finite float array. Parameters ---------- array1 : (N, ..., M) ndarray Array 1 in the enumerator. array2 : (N, ..., M) ndarray Array 2 in the denominator. cval : float, optional Value used to replace zero entries in the denominator. Returns ------- array : (N, ..., M) ndarray Quotient of the array division. r)npcopydivide)array1array2cval denominatorr=/tmp/pip-target-vg8gfxp4/lib/python/skimage/filters/ridges.py_divide_nonzeros   rcCs:ttjdd|jD}t||||<|t|S)a Sort array along a given axis by absolute values. Parameters ---------- array : (N, ..., M) ndarray Array with input image data. axis : int Axis along which to sort. Returns ------- array : (N, ..., M) ndarray Array sorted along a given axis by absolute values. Notes ----- Modified from: http://stackoverflow.com/a/11253931/4067734 cSsg|]}t|qSr)r arange).0irrr Ksz_sortbyabs..)listr ix_shapeabsargsorttuple)arrayaxisindexrrr _sortbyabs5s r"cCs(t|}t|dkrtd|S)a0Check sigma values for ridges filters. Parameters ---------- sigmas : iterable of floats Sigmas argument to be checked Returns ------- sigmas : ndarray input iterable converted to ndarray Raises ------ ValueError if any input value is negative gz5Sigma values should be equal to or greater than zero.)r asarrayravelany ValueError)sigmasrrr _check_sigmasTsr(noneconstantcs~t|j}t|}|j|dd}t|d||d}fdd|D}t|}|dkr2t|dd }|S|d kr=tj|dd }|S) a Compute Hessian eigenvalues of nD images. For 2D images, the computation uses a more efficient, skimage-based algorithm. Parameters ---------- image : (N, ..., M) ndarray Array with input image data. sigma : float Smoothing factor of image for detection of structures at different (sigma) scales. sorting : {'val', 'abs', 'none'}, optional Sorting of eigenvalues by values ('val') or absolute values ('abs'), or without sorting ('none'). Default is 'none'. 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 ------- eigenvalues : (D, N, ..., M) ndarray Array with (sorted) eigenvalues of Hessian eigenvalues for each pixel of the input image. Fr rc)sigmaordermodercsg|]}d|qSrr)rer-rrrsz/compute_hessian_eigenvalues..rrr val) rdtyperastyperrr"r sort)imager-sortingr/r float_dtypehessian_elementshessian_eigenvaluesrr2rcompute_hessian_eigenvaluesms  r= Treflectc st|}|j|durd}t|j}|j|dd}|r!t|}t|j|j|}t |D]@\}} t || d||ddkro|gdd<fd d t D} | d } t | t | } t| dk| d} | ||<q/tj|dd S) al Filter an image with the Meijering neuriteness filter. This filter can be used to detect continuous ridges, e.g. neurites, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Calculates the eigenvectors of the Hessian to compute the similarity of an image region to neurites, according to the method described in [1]_. Parameters ---------- image : (N, M[, ..., P]) ndarray Array with input image data. sigmas : iterable of floats, optional Sigmas used as scales of filter alpha : float, optional Frangi correction constant that adjusts the filter's sensitivity to deviation from a plate-like structure. black_ridges : boolean, optional When True (the default), the filter detects black ridges; when False, it detects white ridges. 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 ------- out : (N, M[, ..., P]) ndarray Filtered image (maximum of pixels across all scales). See also -------- sato frangi hessian References ---------- .. [1] Meijering, E., Jacob, M., Sarria, J. C., Steiner, P., Hirling, H., Unser, M. (2004). Design and validation of a tool for neurite tracing and analysis in fluorescence microscopy images. Cytometry Part A, 58(2), 167-176. :DOI:`10.1002/cyto.a.20022` Ng?Fr+rr9r/rr>rcs0g|]tjfddtDddqS)cs$g|]}t|qSr)r roll)rj) coefficients eigenvaluesrrrrsz(meijering...rr3)r sumrange)rrDrEndim)rrrs zmeijering..r3)r(rIrr5r6r r zerosr enumerater=rGrminwheremax) r8r'alpha black_ridgesr/rr:filtered_arrayrr- auxiliaryfilteredrrHr meijerings23  rUc Cst|ddgt|}|st|}t|j}tj|j|j|d}t|D]+\}}t ||d||d^} } t tj | dt | } t| ddk| d||<q%tj|dd S) a Filter an image with the Sato tubeness filter. This filter can be used to detect continuous ridges, e.g. tubes, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Defined only for 2-D and 3-D images. Calculates the eigenvectors of the Hessian to compute the similarity of an image region to tubes, according to the method described in [1]_. Parameters ---------- image : (N, M[, P]) ndarray Array with input image data. sigmas : iterable of floats, optional Sigmas used as scales of filter. black_ridges : boolean, optional When True (the default), the filter detects black ridges; when False, it detects white ridges. 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 ------- out : (N, M[, P]) ndarray Filtered image (maximum of pixels across all scales). See also -------- meijering frangi hessian References ---------- .. [1] Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S., Koller, T., ..., Kikinis, R. (1998). Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. Medical image analysis, 2(2), 143-168. :DOI:`10.1016/S1361-8415(98)80009-1` rr5r4rAr>rJrr3)rr(r rr5r rKrrLr=rmultiplyreducelenrNrO) r8r'rQr/rr:rRrr-lamba1lambdasrTrrrsatos1  r]g?c Cs|dur|durtdddt|d|d|}t|ddgt|}d|d} d|d} d|d} |j} |r?t|}t|j}tj |j |j |d}tj ||d}t |D]g\}}t ||d || d ^}}| dkrptjnt|d}ttj|dt|}t||d}t|dgd d |D}dt| | t| | dt| | ||<tj|dd ||<qZd||dk<tj|dd S)a Filter an image with the Frangi vesselness filter. This filter can be used to detect continuous ridges, e.g. vessels, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Defined only for 2-D and 3-D images. Calculates the eigenvectors of the Hessian to compute the similarity of an image region to vessels, according to the method described in [1]_. Parameters ---------- image : (N, M[, P]) ndarray Array with input image data. sigmas : iterable of floats, optional Sigmas used as scales of filter, i.e., np.arange(scale_range[0], scale_range[1], scale_step) scale_range : 2-tuple of floats, optional The range of sigmas used. scale_step : float, optional Step size between sigmas. alpha : float, optional Frangi correction constant that adjusts the filter's sensitivity to deviation from a plate-like structure. beta : float, optional Frangi correction constant that adjusts the filter's sensitivity to deviation from a blob-like structure. gamma : float, optional Frangi correction constant that adjusts the filter's sensitivity to areas of high variance/texture/structure. black_ridges : boolean, optional When True (the default), the filter detects black ridges; when False, it detects white ridges. 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 ------- out : (N, M[, P]) ndarray Filtered image (maximum of pixels across all scales). Notes ----- Written by Marc Schrijver, November 2001 Re-Written by D. J. Kroon, University of Twente, May 2009, [2]_ Adoption of 3D version from D. G. Ellis, Januar 20017, [3]_ See also -------- meijering sato hessian References ---------- .. [1] Frangi, A. F., Niessen, W. J., Vincken, K. L., & Viergever, M. A. (1998,). Multiscale vessel enhancement filtering. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 130-137). Springer Berlin Heidelberg. :DOI:`10.1007/BFb0056195` .. [2] Kroon, D. J.: Hessian based Frangi vesselness filter. .. [3] Ellis, D. G.: https://github.com/ellisdg/frangi3d/tree/master/frangi NzpUse keyword parameter `sigmas` instead of `scale_range` and `scale_range` which will be removed in version 0.17.r) stacklevelrr>rVrWrrAcSsg|]}|dqSr0r)rlambdairrrrszfrangi..r3)rr rrr(rIr rr5rKr zeros_likerLr=infrrrXrYrZrFexprO)r8r' scale_range scale_steprPbetagammarQr/ralpha_sqbeta_sqgamma_sqrIr:rR lambdas_arrayrr-lambda1r\r_a filtered_rawr_br_grrrfrangifsBF      rqc Cs,t|||||||||| d } d| | dk<| S)aFilter an image with the Hybrid Hessian filter. This filter can be used to detect continuous edges, e.g. vessels, wrinkles, rivers. It can be used to calculate the fraction of the whole image containing such objects. Defined only for 2-D and 3-D images. Almost equal to Frangi filter, but uses alternative method of smoothing. Refer to [1]_ to find the differences between Frangi and Hessian filters. Parameters ---------- image : (N, M[, P]) ndarray Array with input image data. sigmas : iterable of floats, optional Sigmas used as scales of filter, i.e., np.arange(scale_range[0], scale_range[1], scale_step) scale_range : 2-tuple of floats, optional The range of sigmas used. scale_step : float, optional Step size between sigmas. beta : float, optional Frangi correction constant that adjusts the filter's sensitivity to deviation from a blob-like structure. gamma : float, optional Frangi correction constant that adjusts the filter's sensitivity to areas of high variance/texture/structure. black_ridges : boolean, optional When True (the default), the filter detects black ridges; when False, it detects white ridges. 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 ------- out : (N, M[, P]) ndarray Filtered image (maximum of pixels across all scales). Notes ----- Written by Marc Schrijver (November 2001) Re-Written by D. J. Kroon University of Twente (May 2009) [2]_ See also -------- meijering sato frangi References ---------- .. [1] Ng, C. C., Yap, M. H., Costen, N., & Li, B. (2014,). Automatic wrinkle detection using hybrid Hessian filter. In Asian Conference on Computer Vision (pp. 609-622). Springer International Publishing. :DOI:`10.1007/978-3-319-16811-1_40` .. [2] Kroon, D. J.: Hessian based Frangi vesselness filter. ) r'rdrerPrfrgrQr/rr>r)rq) r8r'rdrerPrfrgrQr/rrTrrrhessians? rr)r )r)r)r*r)__doc__warningsrnumpyr _shared.utilsrrfeature.cornerrrutilrr rr"r(r=rGrUr]rqrrrrrrs6    > h S