## Continuous Visibility Feature for Mesh Analysis and Mesh Segmentation

#### Guilin Liu, Yotam Gingold and Jyh-Ming Lien

#### Overview

In this work, we propose a new type of visibility measurement named Continuous Visibility Feature (CVF). We say that a point q on the mesh is continuously visible from another point p if there exists a geodesic path connecting p and q that is entirely visible by p. In order to efficiently estimate the continuous visibility for all vertices in a model, we propose two approaches that use specific CVF properties to avoid exhaustive visibility tests. CVF is then measured as the area of the continuously visible region. With this stronger visibility measure, we show that CVF better encodes the surface and part information of mesh than the tradition line-of-sight based visibility. For example, we show that existing segmentation algorithms can generate better segmentation results using CVF and its variants than using other visibility-based shape descriptors, such as shape diameter function. Similar to visibility and other mesh surface features, continuous visibility would have many applications.

#### Publications

Continuous Visibility Feature, Guilin Liu and Yotam Gingold and Jyh-Ming Lien,

Web Site / Paper (pdf) / BibTeX

*28th IEEE Conference on Computer Vision and Pattern Recognition (CVPR)*, IEEE, Jun. 2015Web Site / Paper (pdf) / BibTeX

#### Definition

A point

*q*is said to be continuously visible from

*p*if there exists a path connecting

*p*to

*q*such that all points along this path are visible by

*p*.

The CVF of a point

*p*is simply the integral of all continuously visible from

*p*.

In a 2D example below,

*r*is continuously visible from

*p*while

*q*is not.

#### Comparison

For each model, the

**left**is SDF; the

**right**is CVF.

#### Code & Data

- Source code: compute CVF given a 3D mesh CVF source code
- Visualizer code & CVF results: Matlab tool for visualizing CVF (3D Mesh Feature Visualization Matlab Code). CVF visualizer

#### Supplemental materials

- Complete segmentation comparison and pseudo code
- Comparison with Shape Diameter Function (SDF)
- Comparison with SDF (43MB)