#!/usr/bin/env python ''' sample for disctrete fourier transform (dft) USAGE: dft.py <image_file> ''' # Python 2/3 compatibility from __future__ import print_function import cv2 import numpy as np import sys def shift_dft(src, dst=None): ''' Rearrange the quadrants of Fourier image so that the origin is at the image center. Swaps quadrant 1 with 3, and 2 with 4. src and dst arrays must be equal size & type ''' if dst is None: dst = np.empty(src.shape, src.dtype) elif src.shape != dst.shape: raise ValueError("src and dst must have equal sizes") elif src.dtype != dst.dtype: raise TypeError("src and dst must have equal types") if src is dst: ret = np.empty(src.shape, src.dtype) else: ret = dst h, w = src.shape[:2] cx1 = cx2 = w/2 cy1 = cy2 = h/2 # if the size is odd, then adjust the bottom/right quadrants if w % 2 != 0: cx2 += 1 if h % 2 != 0: cy2 += 1 # swap quadrants # swap q1 and q3 ret[h-cy1:, w-cx1:] = src[0:cy1 , 0:cx1 ] # q1 -> q3 ret[0:cy2 , 0:cx2 ] = src[h-cy2:, w-cx2:] # q3 -> q1 # swap q2 and q4 ret[0:cy2 , w-cx2:] = src[h-cy2:, 0:cx2 ] # q2 -> q4 ret[h-cy1:, 0:cx1 ] = src[0:cy1 , w-cx1:] # q4 -> q2 if src is dst: dst[:,:] = ret return dst if __name__ == "__main__": if len(sys.argv) > 1: im = cv2.imread(sys.argv[1]) else: im = cv2.imread('../data/baboon.jpg') print("usage : python dft.py <image_file>") # convert to grayscale im = cv2.cvtColor(im, cv2.COLOR_BGR2GRAY) h, w = im.shape[:2] realInput = im.astype(np.float64) # perform an optimally sized dft dft_M = cv2.getOptimalDFTSize(w) dft_N = cv2.getOptimalDFTSize(h) # copy A to dft_A and pad dft_A with zeros dft_A = np.zeros((dft_N, dft_M, 2), dtype=np.float64) dft_A[:h, :w, 0] = realInput # no need to pad bottom part of dft_A with zeros because of # use of nonzeroRows parameter in cv2.dft() cv2.dft(dft_A, dst=dft_A, nonzeroRows=h) cv2.imshow("win", im) # Split fourier into real and imaginary parts image_Re, image_Im = cv2.split(dft_A) # Compute the magnitude of the spectrum Mag = sqrt(Re^2 + Im^2) magnitude = cv2.sqrt(image_Re**2.0 + image_Im**2.0) # Compute log(1 + Mag) log_spectrum = cv2.log(1.0 + magnitude) # Rearrange the quadrants of Fourier image so that the origin is at # the image center shift_dft(log_spectrum, log_spectrum) # normalize and display the results as rgb cv2.normalize(log_spectrum, log_spectrum, 0.0, 1.0, cv2.NORM_MINMAX) cv2.imshow("magnitude", log_spectrum) cv2.waitKey(0) cv2.destroyAllWindows()