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Additional info for Channel-coded feature maps for computer vision and machine learning
For all continuous reconstruction experiments, peaks were detected from the raw reconstruction p as well as from B ∗ p (with the second-order B-spline kernel B) and from BVS ∗ p. Note that BVS is wider than B. To measure the discrimination threshold, two values x0 ± d were encoded. The discrimination threshold in this context is defined as the minimum value of d which gives two distinct peaks in the reconstruction. As the background DC level increases, the distribution becomes closer to uniform, and the performance of the MEM and MN methods is expected to become increasingly similar.
This direction is not followed further. 3 Bhattacharyya Coefficient Let p1 (x) and p2 (x) be two continuous density functions. 6) −∞ and the Bhattacharyya distance as B(p1 , p2 ) = − ln ρ(p1 , p2 ). This is not a distance measure in a strict sense, since the triangle inequality is not satisfied . 7) which can be identified as a measure proportional to the Euclidean distance between the point-wise square-roots of the densities: √ √ p1 − p2 = ∞ 1/2 2 p1 (x) − p2 (x) dx = −∞ 1/2 ∞ p1 (x) − 2 p1 (x) p2 (x) + p2 (x) dx −∞ 1/2 (2 − 2ρ(p1 , p2 )) = √ 2 d(p1 , p2 ) .
The entire tracking algorithm is summarized as Alg. 1. Note that the derivatives from previous section are relative to the (u, v) coordinate system. 31) . 32) The constant k represents the scale change between the coordinate systems. If the (x, y) system is measured in image pixels, k −1 is pixels per channel-spacing unit. 33) . 1 Tracking using channel-coded feature maps. Inputs: - Target CCFM c0 - Estimated similarity frame ψ k−1 from previous image - New image Ik . Initialize ψ k = ψ k−1 repeat Extract features ck = f (ψ k ) with derivatives J from image Ik s = (JT J)−1 JT (ck − c0 ) Determine α by a line search in the direction s ψ k = ψ k + αs until α is small enough or max iterations reached No coordinate system compensation is required for the rotation and scale derivatives.