780 research outputs found
Making Laplacians commute
In this paper, we construct multimodal spectral geometry by finding a pair of
closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are
jointly diagonalizable and hence have the same eigenbasis. Our construction
naturally extends classical data analysis tools based on spectral geometry,
such as diffusion maps and spectral clustering. We provide several synthetic
and real examples of applications in dimensionality reduction, shape analysis,
and clustering, demonstrating that our method better captures the inherent
structure of multi-modal data
Multidimensional Scaling on Multiple Input Distance Matrices
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial
representations for data points, given the pairwise distances between them.
However, in recent years, data are usually collected from diverse sources or
have multiple heterogeneous representations. How to do multidimensional scaling
on multiple input distance matrices is still unsolved to our best knowledge. In
this paper, we first define this new task formally. Then, we propose a new
algorithm called Multi-View Multidimensional Scaling (MVMDS) by considering
each input distance matrix as one view. Our algorithm is able to learn the
weights of views (i.e., distance matrices) automatically by exploring the
consensus information and complementary nature of views. Experimental results
on synthetic as well as real datasets demonstrate the effectiveness of MVMDS.
We hope that our work encourages a wider consideration in many domains where
MDS is needed
Self-correction of 3D reconstruction from multi-view stereo images
We present a self-correction approach to improving the
3D reconstruction of a multi-view 3D photogrammetry system.
The self-correction approach has been able to repair
the reconstructed 3D surface damaged by depth discontinuities.
Due to self-occlusion, multi-view range images
have to be acquired and integrated into a watertight nonredundant
mesh model in order to cover the extended surface
of an imaged object. The integrated surface often suffers
from “dent” artifacts produced by depth discontinuities
in the multi-view range images. In this paper we propose
a novel approach to correcting the 3D integrated surface
such that the dent artifacts can be repaired automatically.
We show examples of 3D reconstruction to demonstrate the
improvement that can be achieved by the self-correction
approach. This self-correction approach can be extended
to integrate range images obtained from alternative range
capture devices
- …