This paper introduces a topological approach to local invariant feature detection motivated by Morse theory. We use the critical points of the graph of the intensity image, revealing directly the topology information as initial ``interest'' points. Critical points are selected from both the connected components of the upper level sets of the image (the Max-tree) and those of the lower level sets (the Min-tree). They correspond to specific nodes on those two trees: (1) to the leaves (extrema) and (2) to the nodes having bifurcation (saddle points). We then associate to each critical point the largest region that contains it and is topologically equivalent in its tree. We call such largest regions the Tree-Based Morse Regions (TBMR).
TBMR can be seen as a variant of MSER, which are contrasted regions. TBMR relies only on topological information and hence extracts the regions independently of the contrast, which makes it truly contrast invariant and quasi-parameter free. TBMR extraction is fast, having the same complexity as MSER. Experimentally, TBMR achieves a repeatability on par with state-of-the-art methods, but obtains a significantly higher number of features. Both the accuracy and the robustness of TBMR are demonstrated by applications to image registration and 3D reconstruction.
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My name is Laurent Najman and I am a Professor at Université Paris-Est, LIGM, ESIEE.
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