o jk @s8dZddgZddlZddlmZmZddZddZdS)z2 :author: Gary Ruben, 2009 :license: modified BSD frt2ifrt2N)rollnewaxiscCs|jdks|jd|jdkrtd|}|jd}t|d|ftj}|jdd|d<td|D]}td|D] }t ||| ||<q;|jdd||<q4|jdd||<|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 arrayZaxis) ndimshape ValueErrorcopynpemptyuint32sumrangeraZainfmrowri/var/www/html/Deteccion_Ine/venv/lib/python3.10/site-packages/skimage/transform/finite_radon_transform.pyr s* cCs|jdks|jd|jddkrtd|dd}|jd}t||ftj}|jdd|d<td|D]}td|jdD] }t |||||<qB|jdd||<q8||dt j 7}||d|}|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) rrrz0Input must be an (n+1) row x n column, 2-D arrayNr) r r r r r rrrrrrTrrrrrFs"0 )__doc____all__numpyr rrrrrrrrs  :