Smooth point-set registration using neighboring constraints

Abstract

We present an approach for Maximum Likelihood estimation of correspondence and alignment parameters that benefits from the representational skills of graphs. We pose the problem as one of mixture modelling within the framework of the Expectation-Maximization algorithm. Our mixture model encompasses a Gaussian density to model the point-position errors and a Bernoulli density to model the structural errors. The Gaussian density components are parameterized by the alignment parameters which constrain their means to move according to a similarity transformation model. The Bernoulli density components are parameterized by the continuous correspondence indicators which are updated within an annealing procedure using Softassign. Outlier rejection is modeled as a gradual assignment to the null node. We highlight the analogies of our method to some existing methods.We investigate the benefits of using structural and geometrical information by presenting results of the full rigid version of our method together with its pure geometrical and its pure structural versions. We compare our method to other point-set registration methods as well as to other graph matching methods which incorporate geometric information. We also present a non-rigid version of our method and compare to state-of-the art non-rigid registration methods. Results show that our method gets either the best performance or similar performance than state-of-the art methods.

Graph Edit Distance: Moving from global to local structure to solve the graph-matching problem

“…Although in this paper we concretise in the sub-optimal computation of the GED, some other methods have been proposed for specific graph definitions such as planar graphs [32], [33], bounded-valence graphs [34], unique node labels [35] or image registration [36], [37].…”

An interactive method for the image alignment problem based on partially supervised correspondence

“…There is an evaluation of the most competent approaches in Mikolajczyk and Schmid (2005). When salient points have been detected, several correspondence methods can be applied that obtain the alignment (or homography) that maps one image into the other (Zhang, 1994), discards outlier points (Fischler & Bolles, 1981) or characterises the image into an attributed graph Sanromà, Alquézar, Serratosa, & Herrera, 2012).…”

“…In the first case, it is assumed the whole image (and so, the extracted salient points) suffers from the same deformation and so the image alignment parameters are applied equally to all the salient points or image pixels. Some examples are Luo and Hancock (2003), , Sanromà, Alquézar, Serratosa, and Herrera (2012) and Gold and Rangarajan (1996). In the second case, each salient points suffers a different projection and there are different alignment parameters applied to each salient point or image region.…”

Accurate non-rigid registration based on heuristic tree for registering point sets with large deformation

“…Meanwhile, in the non-rigid case, the coherent point drift (CPD) [18] imposed the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. Moreover, some scholars extended to graph matching methods, and applied them to correspondence detection of general images [19,20]. However, the abovementioned methods are effective for the images that have similar structures or appearances, but when the images bear large deformations, the registration doesn't accomplish satisfactory results.…”