Tree-Based Morse Regions: A Topological Approach to Local Feature Detection

From LRDE

Abstract

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 what we call a tree-based shape-space. Specificallythey 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. Contrarily to MSER, TBMR relies only on topological information and thus fully inherit the invariance properties of the space of shapes (em e.g., invariance to affine contrast changes and covariance to continuous transformations). In particular, TBMR extracts the regions independently of the contrast, which makes it truly contrast invariant. Furthermore, it is quasi parameter-free. TBMR extraction is fast, having the same complexity as MSER. ExperimentallyTBMR 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.

Documents

Bibtex (lrde.bib)

@Article{	  xu.14.itip,
  author	= {Yongchao Xu and Thierry G\'eraud and Pascal Monasse and
		  Laurent Najman},
  title		= {Tree-Based Morse Regions: A Topological Approach to Local
		  Feature Detection},
  journal	= {IEEE Transactions on Image Processing},
  year		= {2014},
  volume	= {23},
  number	= {12},
  pages		= {5612--5625},
  month		= dec,
  abstract	= {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 what we call a tree-based shape-space. Specifically,
		  they 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. Contrarily
		  to MSER, TBMR relies only on topological information and
		  thus fully inherit the invariance properties of the space
		  of shapes ({\em e.g.}, invariance to affine contrast
		  changes and covariance to continuous transformations). In
		  particular, TBMR extracts the regions independently of the
		  contrast, which makes it truly contrast invariant.
		  Furthermore, it is 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.}
}