Erik Jonsson's Channel-coded feature maps for computer vision and machine PDF

By Erik Jonsson

ISBN-10: 9173939889

ISBN-13: 9789173939881

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For simplicity, assume that the channel centers are located at the positive integers. 22) i where ρ is some robust error norm. 23) leads to an efficient method. This is the error norm shown in Fig. 7. To find extrema of E(x), we seek zeros of the derivative E (x) = 1 I ρ (xi − x) = i 1 I B(xi − x − 1) − B(xi − x + 1) . 24) i We now construct a new set of coefficients cn = cn+1 − cn−1 and have that cn = cn+1 − cn−1 = 1 1 = B(xi − (n + 1)) − I i I = E (n) . 25) This means that the sequence cn is actually the derivative of the error function sampled at the integers.

This feature map is encoded using N channels in each dimension, resulting in N D channels in total. 1: Some useful K-matrices. The topmost row in each matrix corresponds to polynomial order 0. 2: Some examples of which monomials are required for different CCFMs. 2 Complexity Analysis 47 that exactly S channels are active at the same time in each dimension. This gives in total S D active channels for each input pixel. · A) Direct Approach The simplest thing to do is to loop through the image and accumulate the value of each of the S D bins that are active for each pixel position.

We can replace the order of the integration and differentiation and get dc = e−2s dα d [h(. )] du = e−2s dα dA−1 = e−s dα − sin α − cos α hu (. 11) hu = [hu , hv ] . 12) For compactness, the arguments to h and its derivatives have been left out. 9). The differentiation with respect to b proceeds similarly. We get dc = e−2s db d [h(. )] du = −e−2s db hu (. )A−1 du . 13) 32 Channel-Coded Feature Maps In differentiating with respect to s, the product rule gives us dc d(e−2s ) = ds ds = − 2e−2s = − e−2s h(.

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Channel-coded feature maps for computer vision and machine learning by Erik Jonsson

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