hk 4SrSS/rSSKrSSKJrJr SrSrg)z2 :author: Gary Ruben, 2009 :license: modified BSD frt2ifrt2N)rollnewaxiscURS:wd URSURS:wa [S5eUR5nURSn[R "US-U4[R 5nURSS9US'[SU5H8n[SU5Hn[XU*5X'M URSS9X4'M: URSS9X2'U$)aPCompute the 2-dimensional finite Radon transform (FRT) for the input array. Parameters ---------- a : ndarray of int, shape (M, M) Input array. Returns ------- FRT : ndarray of int, shape (M+1, M) Finite Radon Transform array of coefficients. See Also -------- ifrt2 : The two-dimensional inverse FRT. Notes ----- The FRT has a unique inverse if and only if M is prime. [FRT] The idea for this algorithm is due to Vlad Negnevitski. Examples -------- Generate a test image: Use a prime number for the array dimensions >>> SIZE = 59 >>> img = np.tri(SIZE, dtype=np.int32) Apply the Finite Radon Transform: >>> f = frt2(img) References ---------- .. [FRT] A. Kingston and I. Svalbe, "Projective transforms on periodic discrete image arrays," in P. Hawkes (Ed), Advances in Imaging and Electron Physics, 139 (2006) rz!Input must be a square, 2-D arrayaxis) ndimshape ValueErrorcopynpemptyuint32sumrangeraainfmrows b/var/www/fran/franai/venv/lib/python3.13/site-packages/skimage/transform/finite_radon_transform.pyrr sT vv{aggajAGGAJ.<== B  A !a%RYY'A 66q6>AaD 1a[A;C27SD)BGvv1v~  66q6>AD Hc>URS:wd#URSURSS-:wa [S5eUR5SSnURSn[R "X"4[R 5nURSS9US'[SU5HDn[SURS5Hn[XU5X'M URSS9X4'MF X0S[R- nX1SR5- U- nU$)aCompute the 2-dimensional inverse finite Radon transform (iFRT) for the input array. Parameters ---------- a : ndarray of int, shape (M+1, M) Input array. Returns ------- iFRT : ndarray of int, shape (M, M) Inverse Finite Radon Transform coefficients. See Also -------- frt2 : The two-dimensional FRT Notes ----- The FRT has a unique inverse if and only if M is prime. See [1]_ for an overview. The idea for this algorithm is due to Vlad Negnevitski. Examples -------- >>> SIZE = 59 >>> img = np.tri(SIZE, dtype=np.int32) Apply the Finite Radon Transform: >>> f = frt2(img) Apply the Inverse Finite Radon Transform to recover the input >>> fi = ifrt2(f) Check that it's identical to the original >>> assert len(np.nonzero(img-fi)[0]) == 0 References ---------- .. [1] A. Kingston and I. Svalbe, "Projective transforms on periodic discrete image arrays," in P. Hawkes (Ed), Advances in Imaging and Electron Physics, 139 (2006) rrr z0Input must be an (n+1) row x n column, 2-D arrayNr ) r r rrrrrrrrrTrs rrrFs` vv{aggajAGGAJN2KLL #2B  A !#A 66q6>AaD 1a[BHHQK(C27C(BG)vv1v~  2w  A UYY[AA Hr)__doc____all__numpyrrrrrrrr%s' 7 7 t> r