U ?h @s8dZddgZddlZddlmZmZddZddZdS)z2 :author: Gary Ruben, 2009 :license: modified BSD frt2ifrt2N)rollnewaxiscCs|jdks|jd|jdkr&td|}|jd}t|d|ftj}|jdd|d<td|D]8}td|D]}t ||| ||<qv|jdd||<qh|jdd||<|S)aCompute the 2-dimensional finite radon transform (FRT) for an n x n integer array. Parameters ---------- a : array_like A 2-D square n x n integer array. Returns ------- FRT : 2-D ndarray Finite Radon Transform array of (n+1) x n integer coefficients. See Also -------- ifrt2 : The two-dimensional inverse FRT. Notes ----- The FRT has a unique inverse if and only if n 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 ValueErrorcopynpemptyuint32sumrangeraZainfmrowrZ/var/www/html/venv/lib/python3.8/site-packages/skimage/transform/finite_radon_transform.pyr s+ cCs|jdks"|jd|jddkr*td|dd}|jd}t||ftj}|jdd|d<td|D]<}td|jdD]}t |||||<q|jdd||<qp||dt j 7}||d|}|S)ajCompute the 2-dimensional inverse finite radon transform (iFRT) for an (n+1) x n integer array. Parameters ---------- a : array_like A 2-D (n+1) row x n column integer array. Returns ------- iFRT : 2-D n x n ndarray Inverse Finite Radon Transform array of n x n integer coefficients. See Also -------- frt2 : The two-dimensional FRT Notes ----- The FRT has a unique inverse if and only if n 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 rrrrrrTrrrrrGs1" )__doc____all__numpyr rrrrrrrrs ;