convolution

I am seeing a lot of literature in which they say that by using the fft one can reach a faster convolution. I know that one needs to get fft and and then ifft from the results, but I really do not understand why using the fft can make the convolution faster? FFT speeds up convolution for large enough filters, because convolution requires N multiplications (and N-1) additions for each output sample and conversely (2)N^2 operations for a block of N samples. Taking account, that one has to double the block size for FFT processing by adding zeroes, each block requires (2)*(2N)*log(2N) operations

In the paper 'Fully Convolutional Networks for Semantic Segmentation' the author distinguishes between input stride and output stride in the context of deconvolution. How do these terms differ from each other? Input stride is the stride of the filter . How much you shift the filter in the output . Output Stride this is actually a nominal value . We get feature map in a CNN after doing several convolution , max-pooling operations . Let's say our input image is 224 * 224 and our final feature map is 7*7 . Then we say our output stride is : 224/7 = 32 (Approximate of what happened to the image

weights = tf.placeholder("float",[5,5,1,1]) imagein = tf.placeholder("float",[1,32,32,1]) conv = tf.nn.conv2d(imagein,weights,strides=[1,1,1,1],padding="SAME") deconv = tf.nn.conv2d_transpose(conv, weights, [1,32,32,1], [1,1,1,1],padding="SAME") dw = np.random.rand(5,5,1,1) noise = np.random.rand(1,32,32,1) sess = tf.InteractiveSession() convolved = conv.eval(feed_dict={imagein: noise, weights: dw}) deconvolved = deconv.eval(feed_dict={imagein: noise, weights: dw}) I've been trying to figure out conv2d_transpose in order to reverse a convolution in Tensorflow. My understanding is that

In the conv-nets model, I know how to visualize the filters, we can do itorch.image(model:get(1).weight) But how could I efficiently visualize the output images after the convolution? especially those images in the second or third layer in a deep neural network? Thanks. Similarly to weight, you can use: itorch.image(model:get(1).output) To visualize the weights: -- visualizing weights n = nn.SpatialConvolution(1,64,16,16) itorch.image(n.weight) To visualize the feature maps: -- initialize a simple conv layer n = nn.SpatialConvolution(1,16,12,12) -- push lena through net :) res = n:forward

I am trying to use FFTW for image convolution. At first just to test if the system is working properly, I performed the fft, then the inverse fft, and could get the exact same image returned. Then a small step forward, I used the identity kernel(i.e., kernel[0][0] = 1 whereas all the other components equal 0). I took the component-wise product between the image and kernel(both in the frequency domain), then did the inverse fft. Theoretically I should be able to get the identical image back. But the result I got is very not even close to the original image. I am suspecting this has something to

Say we have a single channel image (5x5) A = [ 1 2 3 4 5 6 7 8 9 2 1 4 5 6 3 4 5 6 7 4 3 4 5 6 2 ] And a filter K (2x2) K = [ 1 1 1 1 ] An example of applying convolution (let us take the first 2x2 from A) would be 1*1 + 2*1 + 6*1 + 7*1 = 16 This is very straightforward. But let us introduce a depth factor to matrix A i.e., RGB image with 3 channels or even conv layers in a deep network (with depth = 512 maybe). How would the convolution operation be done with the same filter ? A similiar work out will be really helpful for an RGB case. They will be just the same as how you do with a single