... in processing large batches of images. I implemented the 2D-DFT using repeated 1D-DFT, and it worked fine, but when I tried to implement 2D inverse DFT using repeated inverse 1D-DFT, some weird problem occurred: when I transform an image to its Fourier domain and then back to the image … [U,V] = tforminv(T,X,Y) applies the 2D-to-2D inverse spatial transformation defined in T to coordinate arrays X and Y, mapping the point [X(k) Y(k)] to the point [U(k) V(k)]. Locate your output image pixel grid somewhere in output space.
i have multiplied the Fourier transform of an image F with H. where H is the FT of a
DIP Lecture 2 20. Then for each output pixel on the grid: Apply the inverse spatial transformation to determine the corresponding location in input space: (u k,v k) = T-1 {(x k,y k)}. Geometric transformations are necessary if the imaging process suffers from some inherent geometric distortions.For instance, a high-resolution airborne line scanner, which sweeps each sensor across the terrain below (so called "pushbroom imaging") produces extremely distorted images due to changes in velocity, altitude, and attitude, i.e. by a unified processing of affine transformations, perspective projections, points, and vectors all transformations of points and vectors are represented by a matrix-vector multiplication "undoing" a transformation is represented by its inverse compositing of transformations is accomplished by matrix multiplication Summary Both T.ndims_in and T.ndims_out must equal 2. U and V are the same size as X and Y I am trying to implement, in Python, some functions that transform images to their Fourier domain and vice-versa, for image processing tasks. Colorado School of Mines Image and Multidimensional Signal Processing Use of Wavelets in Processing •Approach: –Compute the 2D wavelet transform –Alter the transform –Compute the inverse transform •Examples: –De-noising –Compression –Image fusion Hadamard transform; Hough transform (digital image processing) Inverse scattering transform; Legendre transformation; Möbius transformation; Perspective transform (computer graphics) Sequential euclidean distance transforms; Watershed transform (digital image processing) Wavelet transform (orthonormal) Y-Δ transform (electrical circuits) See also I have also red from you "Fundamentals of Image Processing". Fourier Transform in Digital Signal Processing. The inverse transform is T−1 = T−1 1 T −1 2 T −1 3 If we find the transform in one direction, we can invert it to go the other way.
It's well known that convolution in the spatial domain is equivalent to multiplication in the frequency domain. DIP Lecture 2 10. X and Y are typically column vectors, but they can have any dimensionality. Jakub Szymanowski.