1-PhQddlZddlmZddlmZddlmZmZm Z m Z ddl m Z ddl mZdd lmZdd lmZdd lmZgd ZddddZdZdZ ddZdZ ddZdS)N)interp1d) golden_ratio)fftifftfftfreqfftshift)warp)sart_projection_update)convert_to_float)warn)partial)radonorder_angles_golden_ratioiradon iradon_sartTF)preserve_rangec  |jdkrtd|tjd}t ||}|rt |jdz}tj|j}tjtjd|jdd|jdft}||dzz dz d}||dzk}tj ||rtdtfd |z D} || } ntjdt|jzfd |jD} d t!|j| D} d |jD} d t!| | D}dt!|| D}tj||dd} | jd| jdkrtd| jddz}tj| jdt'|f|j}t+tj|D]\}}tj|tj|}}tj||| ||zdz zg| || ||z dz zggdg}t3| |d}| d|dd|f<|S)aV Calculates the radon transform of an image given specified projection angles. Parameters ---------- image : ndarray Input image. The rotation axis will be located in the pixel with indices ``(image.shape[0] // 2, image.shape[1] // 2)``. theta : array, optional Projection angles (in degrees). If `None`, the value is set to np.arange(180). circle : boolean, optional Assume image is zero outside the inscribed circle, making the width of each projection (the first dimension of the sinogram) equal to ``min(image.shape)``. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html Returns ------- radon_image : ndarray Radon transform (sinogram). The tomography rotation axis will lie at the pixel index ``radon_image.shape[0] // 2`` along the 0th dimension of ``radon_image``. References ---------- .. [1] AC Kak, M Slaney, "Principles of Computerized Tomographic Imaging", IEEE Press 1988. .. [2] B.R. Ramesh, N. Srinivasa, K. Rajgopal, "An Algorithm for Computing the Discrete Radon Transform With Some Applications", Proceedings of the Fourth IEEE Region 10 International Conference, TENCON '89, 1989 Notes ----- Based on code of Justin K. Romberg (https://www.clear.rice.edu/elec431/projects96/DSP/bpanalysis.html) r The input image must be 2-DNrr dtypezERadon transform: image must be zero outside the reconstruction circlec 3K|]p}|dkrWtttj|dz ttj|dz zntdVqdS)rr N)sliceintnpceil).0excess shape_mins a/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/skimage/transform/radon_transform.py zradon..Os  A::c"'&1*--..BGFQJ4G4G)4S0T0TUUU4[[       cXg|]&}ttj|z 'S)rrr)rsdiagonals r" zradon..Zs/???as278a<(())???r$c$g|] \}}||zdzSr r&)rr'ps r"r)zradon..[s$EEEtq!q1ulEEEr$cg|]}|dzSr+r&)rr's r"r)zradon..\s222a1f222r$cg|] \}}||z  Sr&r&)rocncs r"r)zradon..]s HHH&"bb2gHHHr$c"g|] \}}|||z f Sr&r&)rpbr,s r"r)zradon..^s$DDDeb!b!b&\DDDr$constantmodeconstant_valueszpadded_image must be a square)rrr F)clip)ndim ValueErrorraranger minshapearrayogridobjectsumanyrtuplesqrtmaxzippadzeroslenr enumeratedeg2radcossinr )imagethetacirclerradius img_shapecoordsdistoutside_reconstruction_circleslices padded_imagerF new_center old_center pad_before pad_widthcenter radon_imageianglecos_asin_aRrotatedr(r!s @@r"rrsGV zQ6777 } # UN 3 3E T $$ aHU[)) "(#3U[^#35Eu{1~5E#EFfUUU)q.(Q.33A66(,vqy(8% 6%56 7 7  (        %y0      V} 71::EK 0 00????5;???EEs5;/D/DEEE 22ek222 HHC J,G,GHHH DDs:s/C/CDDD veYZQRSSS ! 21 5558999   "a 'F(L.q13u::>ekRRRKbj//00 + +5ve}}bfUmmu Hw%%-!*;<=55=1+< =>    |QU333#KKNN AAAqD r$cttjtjd|jdz}||jdz }|jddz}|dz}||z }|||z fdf}tj||ddS)Nr rrrr3r4)rrrrCr<rF)sinogramr(rFrXrWrYrZs r"_sinogram_circle_to_squarerfus27271::q(99::;;H X^A& &C"a'JQJj(JcJ./8I 6(IJ J J JJr$c tjtjd|dz dzdttj|dz dz ddtf}tj|}d|d<dtj|zdzz |ddd<dtjt|z}|d krn|d krLtjt|ddz}|ddxxtj ||z zcc<n|d krItj dtj|d }ttj |}||z}n_|dkr%|ttj |z}n4|dkr%|ttj |z}n |d|dd<|ddtjfS)a{Construct the Fourier filter. This computation lessens artifacts and removes a small bias as explained in [1], Chap 3. Equation 61. Parameters ---------- size : int filter size. Must be even. filter_name : str Filter used in frequency domain filtering. Filters available: ramp, shepp-logan, cosine, hamming, hann. Assign None to use no filter. Returns ------- fourier_filter: ndarray The computed Fourier filter. References ---------- .. [1] AC Kak, M Slaney, "Principles of Computerized Tomographic Imaging", IEEE Press 1988. r r rrg?Nramp shepp-logancosineFendpointhamminghann)r concatenater:rrGpirealrrrLlinspacerrohanningnewaxis)size filter_namenffourier_filteromegafreq cosine_filters r"_get_fourier_filterrs4  IaAq 4 4 4 IdQhlAr 5 5 5   A A AaDBEAI!##AaddG Q(Nf  % % abb))qrrbfUmme33  {1beTE::: .. -'  ! !(2:d#3#3444   (2:d#3#3444  qqq !!!RZ- ((r$rjlinearc |jdkrtd|#tjdd|jdd}t |}||jdkrtd d }||vrtd |d } || vrtd |t ||}|j} |jd} |>|r| }n9ttj tj | dzdz }|rt|}|jd} tdtdtj tjd| zz} d| | z fdf} tj|| dd}t!| |}t#|d|z}tjt'|dd| ddf}tj||f| }|dz}tjd|d|f|z \}}tj| | dzz }t/|jtj|D]{\}}|tj|z|tj|zz }|dkrt9tj||dd}nt=|||dd}|||z }||r|dz|dzz|dzk}d||<|tjzd|zz S)a Inverse radon transform. Reconstruct an image from the radon transform, using the filtered back projection algorithm. Parameters ---------- radon_image : ndarray Image containing radon transform (sinogram). Each column of the image corresponds to a projection along a different angle. The tomography rotation axis should lie at the pixel index ``radon_image.shape[0] // 2`` along the 0th dimension of ``radon_image``. theta : array, optional Reconstruction angles (in degrees). Default: m angles evenly spaced between 0 and 180 (if the shape of `radon_image` is (N, M)). output_size : int, optional Number of rows and columns in the reconstruction. filter_name : str, optional Filter used in frequency domain filtering. Ramp filter used by default. Filters available: ramp, shepp-logan, cosine, hamming, hann. Assign None to use no filter. interpolation : str, optional Interpolation method used in reconstruction. Methods available: 'linear', 'nearest', and 'cubic' ('cubic' is slow). circle : boolean, optional Assume the reconstructed image is zero outside the inscribed circle. Also changes the default output_size to match the behaviour of ``radon`` called with ``circle=True``. preserve_range : bool, optional Whether to keep the original range of values. Otherwise, the input image is converted according to the conventions of `img_as_float`. Also see https://scikit-image.org/docs/dev/user_guide/data_types.html Returns ------- reconstructed : ndarray Reconstructed image. The rotation axis will be located in the pixel with indices ``(reconstructed.shape[0] // 2, reconstructed.shape[1] // 2)``. .. versionchanged:: 0.19 In ``iradon``, ``filter`` argument is deprecated in favor of ``filter_name``. References ---------- .. [1] AC Kak, M Slaney, "Principles of Computerized Tomographic Imaging", IEEE Press 1988. .. [2] B.R. Ramesh, N. Srinivasa, K. Rajgopal, "An Algorithm for Computing the Discrete Radon Transform With Some Applications", Proceedings of the Fourth IEEE Region 10 International Conference, TENCON '89, 1989 Notes ----- It applies the Fourier slice theorem to reconstruct an image by multiplying the frequency domain of the filter with the FFT of the projection data. This algorithm is called filtered back projection. r rNrrr FrmzPThe given ``theta`` does not match the number of projections in ``radon_image``.)rnearestcubiczUnknown interpolation: )rjrkrlrorpNzUnknown filter: g@@rdr3r4)axisrr)xpfpleftright)kind bounds_error fill_valueg) r8r9rrtr<rHr rrfloorrCrfrDrlog2rFrrrsrrGmgridr:rETrJrKrLrinterprrr)r\rN output_sizerx interpolationrOr angles_countinterpolation_types filter_typesrrQprojection_size_paddedrZimgr{ projectionradon_filtered reconstructedrPxpryprxcolr^t interpolantout_reconstruction_circles r"rrs]J16777 } AsK$5a$85IIIu::L{(+++ .   9///B=BBCCCML,&&9K99:::";??K  E!!$I  I#KKbhrw a/?#/E'F'FGGHHK )0== %a( !Sbgbga)m6L6L.M.M)M%N%NOO+i78&AI &ij! L L LC))?MMNSq!!!N2JWT*1555jyj!!!mDEENHk;7uEEEM A Fx  l{l23f>(( U "&-- #u "5 5 H $ $!")cKKKKK"3]1K Q'  7%(!Vc1f_ $A!36 /0 25 A $4 55r$c#^Kd}ttj|}||d}|dV|tdzz }|r||}||z|z}tj||}|dz }|t |z}t|||z }t||z|| z} t|||z } t| |z| | z} | | kr||Vn||V|dSdS)aOrder angles to reduce the amount of correlated information in subsequent projections. Parameters ---------- theta : array of floats, shape (M,) Projection angles in degrees. Duplicate angles are not allowed. Returns ------- indices_generator : generator yielding unsigned integers The returned generator yields indices into ``theta`` such that ``theta[indices]`` gives the approximate golden ratio ordering of the projections. In total, ``len(theta)`` indices are yielded. All non-negative integers < ``len(theta)`` are yielded exactly once. Notes ----- The method used here is that of the golden ratio introduced by T. Kohler. References ---------- .. [1] Kohler, T. "A projection access scheme for iterative reconstruction based on the golden section." Nuclear Science Symposium Conference Record, 2004 IEEE. Vol. 6. IEEE, 2004. .. [2] Winkelmann, Stefanie, et al. "An optimal radial profile order based on the Golden Ratio for time-resolved MRI." Medical Imaging, IEEE Transactions on 26.1 (2007): 68-76. rrr r N) listrargsortpopr searchsortedrHabsr;) rNintervalremaining_indicesr^angle_incrementremaining_angles index_above index_below diff_belowdistance_below diff_abovedistance_aboves r"rrFsu@HRZ..// #A& 'E    " """"q0O 5 !23(H4o&6>> !Ao s,--- !1+!>>?? Z(2J(4JKK!1+!>>?? Z(2J(4JKK N * *#'' 44 4 4 4 4#'' 44 4 4 4! 55555r$333333?c|jdkrtd|?|jjdvr|j}nSt dt jt }n*t j|jdvrtdt j|}||d}|jd |jd f}|%t j d d |jd d| }nbt||jd kr.td t|d|jd dt j ||}|t j ||}nC|j|krtd|jd|d|j|krt d|t j ||}|#t j |jd f|}nbt||jd kr.tdt|d|jd dt j ||}|8t|dkrtdt j ||}t|D]V}t||||dd|f||} ||| zz }|"t j||d |d }W|S)u*Inverse radon transform. Reconstruct an image from the radon transform, using a single iteration of the Simultaneous Algebraic Reconstruction Technique (SART) algorithm. Parameters ---------- radon_image : ndarray, shape (M, N) Image containing radon transform (sinogram). Each column of the image corresponds to a projection along a different angle. The tomography rotation axis should lie at the pixel index ``radon_image.shape[0] // 2`` along the 0th dimension of ``radon_image``. theta : array, shape (N,), optional Reconstruction angles (in degrees). Default: m angles evenly spaced between 0 and 180 (if the shape of `radon_image` is (N, M)). image : ndarray, shape (M, M), optional Image containing an initial reconstruction estimate. Default is an array of zeros. projection_shifts : array, shape (N,), optional Shift the projections contained in ``radon_image`` (the sinogram) by this many pixels before reconstructing the image. The i'th value defines the shift of the i'th column of ``radon_image``. clip : length-2 sequence of floats, optional Force all values in the reconstructed tomogram to lie in the range ``[clip[0], clip[1]]`` relaxation : float, optional Relaxation parameter for the update step. A higher value can improve the convergence rate, but one runs the risk of instabilities. Values close to or higher than 1 are not recommended. dtype : dtype, optional Output data type, must be floating point. By default, if input data type is not float, input is cast to double, otherwise dtype is set to input data type. Returns ------- reconstructed : ndarray Reconstructed image. The rotation axis will be located in the pixel with indices ``(reconstructed.shape[0] // 2, reconstructed.shape[1] // 2)``. Notes ----- Algebraic Reconstruction Techniques are based on formulating the tomography reconstruction problem as a set of linear equations. Along each ray, the projected value is the sum of all the values of the cross section along the ray. A typical feature of SART (and a few other variants of algebraic techniques) is that it samples the cross section at equidistant points along the ray, using linear interpolation between the pixel values of the cross section. The resulting set of linear equations are then solved using a slightly modified Kaczmarz method. When using SART, a single iteration is usually sufficient to obtain a good reconstruction. Further iterations will tend to enhance high-frequency information, but will also often increase the noise. References ---------- .. [1] AC Kak, M Slaney, "Principles of Computerized Tomographic Imaging", IEEE Press 1988. .. [2] AH Andersen, AC Kak, "Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm", Ultrasonic Imaging 6 pp 81--94 (1984) .. [3] S Kaczmarz, "Angenäherte auflösung von systemen linearer gleichungen", Bulletin International de l’Academie Polonaise des Sciences et des Lettres 35 pp 355--357 (1937) .. [4] Kohler, T. "A projection access scheme for iterative reconstruction based on the golden section." Nuclear Science Symposium Conference Record, 2004 IEEE. Vol. 6. IEEE, 2004. .. [5] Kaczmarz' method, Wikipedia, https://en.wikipedia.org/wiki/Kaczmarz_method r z#radon_image must be two dimensionalNfdzOnly floating point data type are valid for SART inverse radon transform. Input data is cast to float. To disable this warning, please cast image_radon to float.zDOnly floating point data type are valid for inverse radon transform.F)copyrrr )rnrzShape of theta (z,) does not match the number of projections ()rzShape of image (z1) does not match first dimension of radon_image (z:image dtype does not match output dtype: image is cast to zShape of projection_shifts (z clip must be a length-2 sequence)r8r9rcharrrfloatastyper<rtrHasarrayrGrr r7) r\rNrMprojection_shiftsr7 relaxationrreconstructed_shape angle_index image_updates r"rrskd1>??? }   !T ) )%EE B    HUOOEE % T ) ) U    HUOOE$$U$77K&,Q/1B11EF } AsK$5a$85PUVVV U{(+ + + >s5zz > >&1&7&: > > >    5... },E::: + + + 6u{ 6 62 6 6 6       Ue U UVVV JuE * * *E Hk&7&:%3/@+A+A > >&1&7&: > > >   J'8FFF  t99>>?@@ @z$e,,,077 5 5 -  +  ; ' k *   l**  GE47DG44E Lr$)NT)NNrjrTT)NNNNrN)numpyrscipy.interpolaterscipy.constantsr scipy.fftrrrr_warpsr _radon_transformr _shared.utilsr warningsr functoolsr__all__rrfrrrrr&r$r"rs&&&&&&((((((222222222222444444,,,,,, J I IbEbbbbbJKKK9)9)9)|  H6H6H6H6V858585z    WWWWWWr$