The Generalized Laplacian Distance and Its Applications for Visual Matching

Abstract

The graph Laplacian operator, which originated in spectral graph theory, is commonly used for learning applications such as spectral clustering and embedding. In this paper we explore the Laplacian distance, a distance function related to the graph Laplacian, and use it for visual search. We show that previous techniques such as Matching by Tone Mapping (MTM) are particular cases of the Laplacian distance. Generalizing the Laplacian distance results in distance measures which are tolerant to various visual distortions. A novel algorithm based on linear decomposition makes it possible to compute these generalized distances efficiently. The proposed approach is demonstrated for tone mapping invariant, outlier robust and multimodal template matching.

OATM: Occlusion Aware Template Matching by Consensus Set Maximization

“…To achieve photometric invariance, [13] introduced a fast scheme for matching under non-linear tone mappings, while [10] used the Generalized Laplacian distance, which can handle multi-modal matching. Our method can provide affine photometric invariance, i.e., up to global brightness and contrast changes.…”

Context-Guided Diffusion for Label Propagation on Graphs

“…For instance, diffusion is now a standard tool for removing noise or to highlight salient structures [32]. The graph Laplacian, as a discrete approximation of the generator of the diffusion process on manifolds, i.e., the Laplace-Beltrami operator, is commonly used in spectral clustering and semisupervised learning, which finds applications in object recognition [7,33], image retrieval [10], and segmentation and matting [3,25]. Similarly, stochastic diffusion process on graphs find application in multi-label classification [30] and image retrieval [12].…”