U ?h$t@sddlZddlZddlmZddlmZmZddl m Z m Z ddl m Z ddlmZddlmZdd lmZmZmZd d Zd d ZddZddZGddde e ZdS)N)check_nD_supported_float_type)DescriptorExtractorFeatureDetector)gaussian)rescale) img_as_float) _local_max_ori_distances_update_histogramcCs$||}||||}|||S)z5Compute edgeness (eq. 18 of Otero et. al. IPOL paper))ZhxxZhyyZhxytraceZ determinantrrF/var/www/html/venv/lib/python3.8/site-packages/skimage/feature/sift.py _edgenesssrcCs|d}|d}|d}||d||f||d||f}|d9}|||d|f|||d|f}|d9}||||df||||df}|d9}|||fS)zGradient of a 3D volume at the provided `positions`. For SIFT we only need the gradient at specific positions and do not need the gradient at the edge positions, so can just use this simple implementation instead of numpy.gradient. .r.r .rr ?r)Zvol positionsp0p1p2g0g1g2rrr_sparse_gradients$$$rc Cs|d}|d}|d}d||||f}||d||f||d||f|}|||d|f|||d|f|}||||df||||df|}d||d|d|f||d|d|f||d|d|f||d|d|f} d||d||df||d||df||d||df||d||df} d|||d|df|||d|df|||d|df|||d|df} |||| | | fS)zCompute the non-redundant 3D Hessian terms at the requested positions. Source: "Anatomy of the SIFT Method" p.380 (13) rrrrr g?r) drrrrZtwo_d0h00h11h22h01h02h12rrr_hessian(s.(((,,,r%cCsD|\}}}}}}|\}} } |||} | |||8} | |||8} | d|||7} | |||8} ||||| } ||||| } ||||| }||||| }||||| }||||| }| || | || }| ||| || }| ||| || }tj|||fddS)a2Compute position refinement offsets from gradient and Hessian. This is equivalent to np.linalg.solve(-H, J) where H is the Hessian matrix and J is the gradient (Jacobian). This analytical solution is adapted from (BSD-licensed) C code by Otero et. al (see SIFT docstring References). rZaxis)npstack)gradhessrr r!r"r#r$rrrZdetZaaabacZbbbcccZoffset0Zoffset1Zoffset2rrr_offsets>s"   r0c @seZdZdZd+ddZeddZddZddZddZ ddZ ddZ ddZ ddZ d d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*S),SIFTuSIFT feature detection and descriptor extraction. Parameters ---------- upsampling : int, optional Prior to the feature detection the image is upscaled by a factor of 1 (no upscaling), 2 or 4. Method: Bi-cubic interpolation. n_octaves : int, optional Maximum number of octaves. With every octave the image size is halved and the sigma doubled. The number of octaves will be reduced as needed to keep at least 12 pixels along each dimension at the smallest scale. n_scales : int, optional Maximum number of scales in every octave. sigma_min : float, optional The blur level of the seed image. If upsampling is enabled sigma_min is scaled by factor 1/upsampling sigma_in : float, optional The assumed blur level of the input image. c_dog : float, optional Threshold to discard low contrast extrema in the DoG. It's final value is dependent on n_scales by the relation: final_c_dog = (2^(1/n_scales)-1) / (2^(1/3)-1) * c_dog c_edge : float, optional Threshold to discard extrema that lie in edges. If H is the Hessian of an extremum, its "edgeness" is described by tr(H)²/det(H). If the edgeness is higher than (c_edge + 1)²/c_edge, the extremum is discarded. n_bins : int, optional Number of bins in the histogram that describes the gradient orientations around keypoint. lambda_ori : float, optional The window used to find the reference orientation of a keypoint has a width of 6 * lambda_ori * sigma and is weighted by a standard deviation of 2 * lambda_ori * sigma. c_max : float, optional The threshold at which a secondary peak in the orientation histogram is accepted as orientation lambda_descr : float, optional The window used to define the descriptor of a keypoint has a width of 2 * lambda_descr * sigma * (n_hist+1)/n_hist and is weighted by a standard deviation of lambda_descr * sigma. n_hist : int, optional The window used to define the descriptor of a keypoint consists of n_hist * n_hist histograms. n_ori : int, optional The number of bins in the histograms of the descriptor patch. Attributes ---------- delta_min : float The sampling distance of the first octave. It's final value is 1/upsampling. float_dtype : type The datatype of the image. scalespace_sigmas : (n_octaves, n_scales + 3) array The sigma value of all scales in all octaves. keypoints : (N, 2) array Keypoint coordinates as ``(row, col)``. positions : (N, 2) array Subpixel-precision keypoint coordinates as ``(row, col)``. sigmas : (N, ) array The corresponding sigma (blur) value of a keypoint. scales : (N, ) array The corresponding scale of a keypoint. orientations : (N, ) array The orientations of the gradient around every keypoint. octaves : (N, ) array The corresponding octave of a keypoint. descriptors : (N, n_hist*n_hist*n_ori) array The descriptors of a keypoint. Notes ----- The SIFT algorithm was developed by David Lowe [1]_, [2]_ and later patented by the University of British Columbia. Since the patent expired in 2020 it's free to use. The implementation here closely follows the detailed description in [3]_, including use of the same default parameters. References ---------- .. [1] D.G. Lowe. "Object recognition from local scale-invariant features", Proceedings of the Seventh IEEE International Conference on Computer Vision, 1999, vol.2, pp. 1150-1157. :DOI:`10.1109/ICCV.1999.790410` .. [2] D.G. Lowe. "Distinctive Image Features from Scale-Invariant Keypoints", International Journal of Computer Vision, 2004, vol. 60, pp. 91–110. :DOI:`10.1023/B:VISI.0000029664.99615.94` .. [3] I. R. Otero and M. Delbracio. "Anatomy of the SIFT Method", Image Processing On Line, 4 (2014), pp. 370–396. :DOI:`10.5201/ipol.2014.82` Examples -------- >>> from skimage.feature import SIFT, match_descriptors >>> from skimage.data import camera >>> from skimage.transform import rotate >>> img1 = camera() >>> img2 = rotate(camera(), 90) >>> detector_extractor1 = SIFT() >>> detector_extractor2 = SIFT() >>> detector_extractor1.detect_and_extract(img1) >>> detector_extractor2.detect_and_extract(img2) >>> matches = match_descriptors(detector_extractor1.descriptors, ... detector_extractor2.descriptors, ... max_ratio=0.6) >>> matches[10:15] array([[ 10, 412], [ 11, 417], [ 12, 407], [ 13, 411], [ 14, 406]]) >>> detector_extractor1.keypoints[matches[10:15, 0]] array([[ 95, 214], [ 97, 211], [ 97, 218], [102, 215], [104, 218]]) >>> detector_extractor2.keypoints[matches[10:15, 1]] array([[297, 95], [301, 97], [294, 97], [297, 102], [293, 104]]) r皙?rO贁N? $?皙?cCs|dkr||_ntd||_||_|||_||_dd|dd||_||_||_| |_ | |_ | |_ | |_ | |_ d||_d|_d|_d|_d|_d|_d|_d|_d|_d|_dS)N)r rr;zupsampling must be 1, 2 or 4rr g,5拢?) upsampling ValueError n_octavesn_scales sigma_minsigma_inc_dogc_edgen_bins lambda_oric_max lambda_descrn_histn_ori delta_min float_dtypescalespace_sigmas keypointsrsigmasscales orientationsoctaves descriptors)selfr<r>r?r@rArBrCrDrErFrGrHrIrrr__init__s2  z SIFT.__init__cCs$|jtjdt|j|jd}|S)z%The sampling distances of all octavesrdtype)rJr(poweraranger>rK)rSdeltasrrrrYsz SIFT.deltascCs<d}t||j}tt||d}||jkr8||_dS)N r )minr<intmathlog2r>)rSZ image_shapeZsize_mins0Z max_octavesrrr_set_number_of_octavess  zSIFT._set_number_of_octavesc Csg}|jdkrt||jdd}t||jt|jd|jddd}tdt |j d|j }||j9}|j ddtj f|j d|tj ddf}||_ tj||dd }t||j ddtj f}t|jD]}tj|j df|j|jd d }||d<td|j dD].} t|| d||| dfd|| d q|t|dd ||jdkr||j ddddddf}q|S)zSource: "Anatomy of the SIFT Method" Alg. 1 Construction of the scalespace by gradually blurring (scales) and downscaling (octaves) the image. r )orderrZreflectmoder3Nrr'C)rVra)rcoutputr&)r<rrr]sqrtr@rAr(rWrXr?rYnewaxisrLdiffranger>emptyshaperKappendZmoveaxis) rSimageZ scalespacetmprNZvar_diffZgaussian_sigmasooctavesrrr_create_scalespace sF      zSIFT._create_scalespacecCs`|dddfdk|dddf|ddk@|dddfdk@|dddf|ddk@S)Nrr r)rSadimrrr_inrange>s .z SIFT._inrangec# sg}g}g}|jd}tt||jD]8\}\}} tt||} | jdkr`|t dq&|j } d} d} t | D]}|dkr| | | | ddf} t || }t|| }t||}|| dkrqFt|| k| dtdd | Dk}t|| k| ddk}tt||s$qF| |d7<| |d8<qvtjt|| kdd | } |}fd d |D}|| dddf| dddf| ddd ff}|}t d D]&}|d|||dd|f7}q|d|d|d }}}|jd|jd}|j}t||k}t|jd|j}t||||||}t||k}| ||} |||}| dddd f|dddd f| |j}|j|| ddd fft||ddd f} tjt|| ddtjfdk|| ddtjf|kdd }!|||!|| |!d f|| |!q&tdd t|D}"t|"dkrt dt|}t|}t|}||||"fS)aLSource: "Anatomy of the SIFT Method" Alg. 4-9 1) first find all extrema of a (3, 3, 3) neighborhood 2) use second order Taylor development to refine the positions to sub-pixel precision 3) filter out extrema that have low contrast and lie on edges or close to the image borders r9r)rrg333333?Nr cSsg|] }|dqS)r r).0rsrrr jsz0SIFT._find_localize_evaluate..r'csg|] }|qSrr)rwgfinishedrrrxzsrr3r)rr )rrgcSs g|]\}}tt||qSr)r(fulllen)rwiprrrrxszoSIFT found no features. Try passing in an image containing greater intensity contrasts between adjacent pixels.)!rB enumerateziprYr r(Zascontiguousarraysizerlrjrkrirurr%r0 logical_andtupleany logical_orallabsrLsquarerCrastyperKrWrg concatenater} RuntimeError)#rSZdogspaceZ img_shapeZ extrema_posZextrema_scalesZextrema_sigmas thresholdrorpdeltakeysoshapeZrefinement_iterationsZ offset_maxr~r*r+offZwrong_position_posZwrong_position_negvalswrr r"Z sigmaratioZcontrast_thresholdZcontrast_filterZedge_thresholdZ edge_responseZ edge_filteryxrNZ border_filterZoctave_indicesrrzr_find_localize_evaluateBs         2 $   4    zSIFT._find_localize_evaluatecCs0|d|dd|d|dd|dS)z;Refine the position of the peak by fitting it to a parabolarrr r)rShrrr_fitsz SIFT._fitc* CsLg}g}g}g} tj||jd} d} tt||jD]\} \} }|t| || k}t|sfq4||}||}||}| j dd}||}||}d|j |}t d||ddtj fd t}t||ddtj fd|dd|ddf t}tj|j|jd}tjdd |jd}tt|D]}d|dd<tjt||df||dfdt||df||dfdd d d \}}|| d||||f}|| d||||f}|j |jd d}|j |jd d}|||df8}|||df8}tt|t|} tt||dtj}!tt||||d|j ||d}"t|!dtj|jd|j t}#tj ||#|"| t!|dd||ddf}tdD]}$tj"||dd}q|dd}t#j$|dgdd}%t%t&||j't(|k|%|k}&t|&dD]\}}'t|'d|'dt|}(|'|)||(ddtj|j})|)tjkr|)dtj8})|dkr|)| | <n|| ||)| | qD| d7} q>q4t!|||f|_*t!|||f|_+t!|||f|_,t!| |f|_-t!|| f|_.|S)z~Source: "Anatomy of the SIFT Method" Alg. 11 Calculates the orientation of the gradient around every keypoint rUrNrr3rr )r3gUUUUUU?ijTZindexingsparseFcopyir:Zsamerbwrap)/r(Z zeros_likerKrrrYrlgradientrrkrEmaximumrgrr\minimumrjrDr|rir}meshgridrXrfrmodarctan2piexpdivideflooraddatrZconvolvendiZmaximum_filternonzerorrFmaxrrrOrNrPrQ)*rSZ positions_octZ scales_octZ sigmas_octrQgaussian_scalespacegradient_spaceZkeypoint_indicesZkeypoint_anglesZkeypoint_octaverPZ key_countrorprin_octrrOrNrrsigmaradiusp_minp_maxhistZ avg_kernelkrc gradient_row gradient_col magnitudethetakernelbins_Z max_filtermaximamZneighorirrr_compute_orientations  "            zSIFT._compute_orientationcCs>t|}t|}||||}| |||}||fS)N)r]cossin)rSrowcolZanglerrqZrot_rowZrot_colrrr_rotate s   z SIFT._rotatec0 Cst|j}tj||jd|jftjd|_tjd|jd|j d}tjd|jd|j d}t|}t t ||j D]\}\}}|j |k} t| sqv|j| } |j| } |j| } |j| } || }|djdd}| |}| |}|jdd|j|}td|}tjtd||ddtjfdtd}tjt||ddtjfd|dd|ddftd}tt|D]|}||}| |}tj|j|j|jf|j d}tjt||df||dft||df||dfddd \}}tj|||df|j d}tj|||df|j d}||||\}}tt |t ||k}||||}}t!|\}} ||df}|d| f}|d||| |f}!|d||| |f}"t"|"|!|}#|j||}$t#||||d |$d}%t|!|!|"|"|%}&d|$|j}'|d|jd|'}(|'})dtj$||j}*t tj%|(|}+t tj%|(|},t&|*|#\}-}.t'||-|.|&|+|,|)|(d }t|d tj)*|}d |tj)*|}/tt+|/d}/|/|j||ddf<qqvdS)zjSource: "Anatomy of the SIFT Method" Alg. 12 Calculates the descriptor for every keypoint rrUr rNrrTrrr&g?i),r}rOr(rjrHrIZuint8rRrXrKrrrYrQrrrNrPrkrGr]rfZasarrayrrgr\rriZzerosrsubtractrrrrrrouterr r ZreshapeZlinalgZnormr)0rSrZn_keyZhistsrZ key_numbersrorrrrrOrNrPnumbersrtZ center_posrrZ radius_patchrrrZrad_krZ histogramsrrZr_normZc_normZinsideZr_idxZc_idxrrrZlam_sigrrZ lam_sig_ratioZrc_binsZrc_bin_spacingZori_binsZdist_rZdist_cZnear_tZ near_t_valZ descriptorrrr_compute_descriptor's                zSIFT._compute_descriptorcCs>t|dt|}t|j|_|j|jdd}||j|S)NrFr)rr rrVrKrr`rk)rSrmrrr _preprocesss    zSIFT._preprocesscCs`||}||}dd|D}|||j\}}}}|||||||jt|_ dS)zxDetect the keypoints. Parameters ---------- image : 2D array Input image. cSsg|]}tj|ddqSrr'r(rhrwlayerrrrrxszSIFT.detect..N) rrrrrkrrroundrr\rM)rSrmrdog_scalespacerrOrNrQrrrdetects    z SIFT.detectcCs0||}||}dd|D}||dS)zExtract the descriptors for all keypoints in the image. Parameters ---------- image : 2D array Input image. cSsg|]}t|qSr)r(r)rwrprrrrxsz SIFT.extract..N)rrrr)rSrmrrrrrextracts  z SIFT.extractc Csj||}||}dd|D}|||j\}}}}||||||}|||jt |_ dS)zDetect the keypoints and extract their descriptors. Parameters ---------- image : 2D array Input image. cSsg|]}tj|ddqSrrrrrrrxsz+SIFT.detect_and_extract..N) rrrrrkrrrrrr\rM) rSrmrrrrOrNrQrrrrdetect_and_extracts     zSIFT.detect_and_extractN) rr2r3r4rr5r6r7r8r9r:r;r2)__name__ __module__ __qualname____doc__rTpropertyrYr`rrrurrrrrrrrrrrrrr1Zs6  4lnc r1)r]numpyr(Z scipy.ndimageZndimagerZ _shared.utilsrrZ feature.utilrrZ_shared.filtersrZ transformrutilr Z_siftr r r rrr%r0r1rrrrs