Probabilistic Correspondence Matching using Random Walk with Restart

Abstract

This paper presents a probabilistic method for correspondence matching with a framework of the random walk with restart (RWR). The matching cost is reformulated as a corresponding probability, which enables the RWR to be utilized for matching the correspondences. There are mainly two advantages in our method. First, the proposed method guarantees the non-trivial steady-state solution of a given initial matching probability due to the restarting term in the RWR. It means the number of iteration, a crucial parameter which influences the performance of algorithm, is not needed in contrast to the conventional methods. This gives the consistent results regardless of the evolution time. Second, only an adjacent neighborhood is considered when the matching probabilities are inferred, which lowers the computational complexity while not sacrificing performance. Experimental results show that the performance of the proposed method is competitive to that of state-of-the-art methods both qualitatively and quantitatively.

Adaptable Precomputation for Random Walker Image Segmentation and Registration

“…Further, the RW algorithm was shown by Couprie et al to be part of a family of graph-based algorithms [5], including other popular algorithms such as Graph Cuts [4]. Random walks have also been applied to other imaging tasks, such as stereo matching [32] and shape correspondence [33]. Our future work will focus on extending our precomputation techniques to the extensions of the RW algorithm, similar graph-based algorithms, and other imaging applications mentioned above.…”

“…We note that the vectors generated by (33) will not form an orthonormal set, but are made so using the Gram-Schmidt process. Combining the orthonormal vectors into a matrix Q and then calculating their corresponding Ncut values allows fastRW to be run on the aggregate graph with minimal overhead and loss in accuracy.…”

“…In this section, we evaluate our technique for aggregating the eigenvectors into super-vertices, given by (33) in Sec. III-C. We use m = 2500 eigenvectors for fastRWIR.…”

“…7), and thus the aggregation must be performed online, after the precomputation. For each pair of thigh and brain images, we run 4 registration schemes: basic RWIR, fastRWIR with the eigenvectors aggregated using the naïve technique in (31), fastRWIR with the eigenvectors aggregated using our proposed technique in (33), and using eigenvectors calculated from the Laplacian of the aggregated graph directly (used only as a baseline, since the aggregated graph is not known offline). The accuracy and run-time of each technique is seen in Fig.…”

Self-Supervised Stereo Matching Method Based on SRWP and PCAM for Urban Satellite Images

“…Hosni et al [13] proposed a fast cost volume filtering stereo matching (FCVFSM) method to realize a real-time disparity map by using fast edge preserving filtering to smooth label costs. In addition to this, some scholars have also started from other perspectives, such as Changjae et al [14], who considered the matching cost as the probability of matching between points and sought the steady-state distribution of the matching probability through the proposed random walk with restart algorithm, thus giving the confidence of their matching along with the output matching result.…”