Hallucinating optimal high-dimensional subspaces

Abstract

Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope of variations within sets of images of different (possibly greatly so) scales. A naïve solution of projecting the lowscale subspace into the high-scale image space is described first and subsequently shown to be inadequate, especially at large scale discrepancies. A successful approach is proposed instead. It consists of (i) an interpolated projection of the low-scale subspace into the highscale space, which is followed by (ii) a rotation of this initial estimate within the bounds of the imposed "downsampling constraint". The optimal rotation is found in the closedform which best aligns the high-scale reconstruction of the low-scale subspace with the reference it is compared to. The method is evaluated on the problem of matching sets of (i) face appearances under varying illumination and (ii) object appearances under varying viewpoint, using two large data sets. In comparison to the naïve matching, the proposed algorithm is shown to greatly increase the separation of between-class and within-class similarities, as well as produce far more meaningful modes of common appearance on which the match score is based.

Tuberculosis Bacteria Detection and Counting in Fluorescence Microscopy Images Using a Multi-Stage Deep Learning Pipeline

“…Following experimental results reported in previous work [33], we used input image patches with the size of 256 × 256 pixels and additionally re-scaled them to 384 × 384 pixels using bicubic interpolation [34], which was found to effect an improvement in performance. We also introduced alterations to the network architecture by including three further residual blocks as a means of improving the detection of bacteria with lower brightness.…”

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“…These correspond to different exemplars f xy in Figure 3 and can be compared using the DFFS baseline. If, on the other hand, similarity is measured using the maximum correlation between subspace spans [32], the most similar modes of variation between two sets are readily extracted as the first pair of the canonical vectors between subspaces [33] and compared using the cosine similarity measure [34,35]. For manifold-to-manifold distances such as that of Lee et al [36] the most similar modes of variation are simply the nearest pairs of points on two manifolds, with the similarity of two points on the same manifold readily quantified by the geodesic distance between them.…”

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