Graphical Models and Point Pattern Matching

Abstract

Abstract-This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes.

3D Object Detection and Viewpoint Selection in Sketch Images Using Local Patch-Based Zernike Moments

“…Although only rigid transformations preserve distances, which are checked by our method, a very large class of nonrigid transformations is handled by the gausians kernels in equation (4) and the fact that interactions between neighbors are verified as opposed to more arbitrary interactions, as for instance in [15].…”

“…1) have been proposed: e.g by adopting the neighborhood structure in order to find the maximum a posteriori solution with the junction tree algorithm [15], which is of complexity O(M · S 4 ) and applicable to few primitives only; or by formulating the problem as a sampling procedure and checking for the consistency of each sample (RANSAC) [18,3]. Instead of solving the full problem, we propose to proceed in two steps:…”

“…We used 4 storyboards of size 3350×2260 for testing. We chose the same variance parameter which has been used in [15] for Gaussian kernels measuring differences in euclidean distances: σ de =σ za =0.4. The choice of an optimal parameter σ is far from trivial [16] and beyond the scope of this paper.…”

Visual features for vehicle localization and ego-motion estimation

“…Other methods like the ones proposed by van Wamelen et al [23] or Caetano et al [5] do not have these restrictions, however they require a large amount of memory and computing time to find the global optimum. Therefore, these methods are not suitable for real-time vehicle localization.…”

Real-Time Exact Graph Matching with Application in Human Action Recognition

“…Formulations like the one in (1) are known to be NP-hard [20]. In the context of object recognition, a method which approximates the graph, which in turn enables computation of the exact solution in polynomial time has been proposed in [22]: a k-tree is built randomly from the spatial interest points on an object, which allows for the application of the classical junction tree algorithm [23]. Spectral methods like the one in [24] relax the binary assignment problem into a continuous one and show that the solution for the continuous problem is the principal eigenvector of the constraints matrix.…”