khk 4dZddgZddlZddlmZmZdZdZy)z2 :author: Gary Ruben, 2009 :license: modified BSD frt2ifrt2N)rollnewaxisc|jdk7s|jd|jdk7r td|j}|jd}t j |dz|ftj }|jd|d<td|D];}td|D]}t||| ||<|jd||<=|jd||<|S)aCompute 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 /home/developers/rajanand/mypropertyqr-fmb-refixing-v2/venv/lib/python3.12/site-packages/skimage/transform/finite_radon_transform.pyrr sT vv{aggajAGGAJ.<== B  A !a%RYY'A 66q6>AaD 1a[A; *C2c7SD)BsG *vv1v~!  66q6>AaD HcH|jdk7s"|jd|jddzk7r td|jdd}|jd}t j ||ftj }|jd|d<td|D]G}td|jdD]}t|||||<|jd||<I||dtjz }||djz |z }|S)aFCompute 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 !Q#A 66q6>AaD 1a[BHHQK( )C2c7C(BsG )vv1v~!  2w  A RUYY[AA Hr)__doc____all__numpyrrrrrrrr%s' 7 7 t> r