convolution

I have convoluted an image I created in matlab with a 2D Gaussian function which I have also defined in matlab and now I am trying to deconvolve the resultant matrix to see if I get the 2D Gaussian function back using the fft2 and ifft2 commands. However the matrix I get as a result is incorrect (to my knowledge). Here is the code for what I have done thus far: % Code for input image (img) [300x300 array] N = 100; t = linspace(0,2*pi,50); r = (N-10)/2; circle = poly2mask(r*cos(t)+N/2+0.5, r*sin(t)+N/2+0.5,N,N); img = repmat(circle,3,3); % Code for 2D Gaussian Function with c = 0 sig = 1/64 (Z)

I'm working on image processing with CUDA and i've a doubt about pixel processing. What is often done with the boundary pixels of an image when applying a m x m convolution filter? In a 3 x 3 convolution kernel, ignoring the 1 pixel boundary of the image is easier to deal with, especially when the code is improved with shared memory. Indeed, in this case, one does not need to check if a given pixel has all the neigbourhood available (i.e. pixel at coord (0, 0) has not left, left-upper, upper neighbours). However, removing the 1 pixel boundary of the original image could generate partial

I know that, in the 1D case, the convolution between two vectors, a and b , can be computed as conv(a, b) , but also as the product between the T_a and b , where T_a is the corresponding Toeplitz matrix for a . Is it possible to extend this idea to 2D? Given a = [5 1 3; 1 1 2; 2 1 3] and b=[4 3; 1 2] , is it possible to convert a in a Toeplitz matrix and compute the matrix-matrix product between T_a and b as in the 1-D case? Salvador Dali Yes, it is possible and you should also use a doubly block circulant matrix (which is a special case of Toeplitz matrix). I will give you an example with a

Can anyone please clearly explain the difference between 1D, 2D, and 3D convolutions in CNN (Deep Learning) with examples? I want to explain with picture from C3D . In a nutshell, convolutional direction & output shape is important! ↑↑↑↑↑ 1D Convolutions - Basic ↑↑↑↑↑ just 1 -direction (time-axis) to calculate conv input = [W], filter = [k], output = [W] ex) input = [1,1,1,1,1], filter = [0.25,0.5,0.25], output = [1,1,1,1,1] output-shape is 1D array example) graph smoothing tf.nn.conv1d code Toy Example import tensorflow as tf import numpy as np sess = tf.Session() ones_1d = np.ones(5) weight

My main goal is to show that the convolution theorem works (just a reminder: the convolution theorem means that idft(dft(im) .* dft(mask)) = conv(im, mask) ). I'm trying to program that. Here is my code: function displayTransform( im ) % This routine displays the Fourier spectrum of an image. % % Input: im - a grayscale image (values in [0,255]) % % Method: Computes the Fourier transform of im and displays its spectrum, % (if F(u,v) = a+ib, displays sqrt(a^2+b^2)). % Uses display techniques for visualization: log, and stretch values to full range, % cyclic shift DC to center (use fftshift). %

I have been trying to do Convolution of a 2D Matrix using SciPy, and Numpy but have failed. For SciPy I tried, sepfir2d and scipy.signal.convolve and Convolve2D for Numpy. Is there a simple function like conv2 in Matlab for Python? Here is an example: A= [ 5 4 5 4; 3 2 3 2; 5 4 5 4; 3 2 3 2 ] I want to convolve it with [0.707 0.707] And the result as by conv2 from Matlab is 3.5350 6.3630 6.3630 6.3630 2.8280 2.1210 3.5350 3.5350 3.5350 1.4140 3.5350 6.3630 6.3630 6.3630 2.8280 2.1210 3.5350 3.5350 3.5350 1.4140 Some function to compute this output in Python? I will be grateful for a response.

in my previous question on finding a reference audio sample in a bigger audio sample, it was proposed, that I should use convolution. Using DSPUtil , I was able to do this. I played a little with it and tried different combinations of audio samples, to see what the result was. To visualize the data, I just dumped the raw audio as numbers to Excel and created a chart using this numbers. A peak is visible, but I don't really know how this helps me. I have these problems: I don't know, how to infer the starting position of the match in the original audio sample from the location of the peak. I