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 small size of kernel and the input, but it is possible to construct Toeplitz matrix for any kernel. So you have a 2d input x … Read more
I think the problem is that you did not do what SciPy implemented. I won’t dwell on the details or the foundations but only provide you with a solution: Reverse the kernel. >>> import numpy as np >>> arr = np.array([[0, 0, 0], [1, 1, 2], [1, 3, 0]]) >>> kernel = np.array([[4, 1, 1], … Read more
Instead of a convolution you should use a correlation. The size of the correlation peak tells you how much both signals are alike, the position of the peak their relative position in time, or the delay between both signals.
There are a number of different ways to do it with scipy, but 2D convolution isn’t directly included in numpy. (It’s also easy to implement with an fft using only numpy, if you need to avoid a scipy dependency.) scipy.signal.convolve2d, scipy.signal.convolve, scipy.signal.fftconvolve, and scipy.ndimage.convolve will all handle a 2D convolution (the last three are N-d) … Read more
Convolution is a mathematical operator primarily used in signal processing. Numpy simply uses this signal processing nomenclature to define it, hence the “signal” references. An array in numpy is a signal. The convolution of two signals is defined as the integral of the first signal, reversed, sweeping over (“convolved onto”) the second signal and multiplied … Read more
The Y array in your screenshot is not a 1D array, it’s a 2D array with 300 rows and 1 column, as indicated by its shape being (300, 1). To remove the extra dimension, you can slice the array as Y[:, 0]. To generally convert an n-dimensional array to 1D, you can use np.reshape(a, a.size). … Read more
Maybe it is not the most optimized solution, but this is an implementation I used before with numpy library for Python: def convolution2d(image, kernel, bias): m, n = kernel.shape if (m == n): y, x = image.shape y = y – m + 1 x = x – m + 1 new_image = np.zeros((y,x)) for … Read more
I finally found a suitable solution: RenderScript allows implementing heavy computations which are scaled transparently to all cores available on the executing device. I’ve come to the conclusion, that with respect to a reasonable balance of performance and implementation complexity, this is a better approach than JNI or shaders. Since API Level 17, there is … Read more
The Discrete Fourier transform (DFT) and, by extension, the FFT (which computes the DFT) have the origin in the first element (for an image, the top-left pixel) for both the input and the output. This is the reason we often use the fftshift function on the output, so as to shift the origin to a … Read more
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 … Read more