---
title: "Intersecting Manifolds: Detection, Segmentation, and Labeling"
authors:
  - "Shay Deutsch"
  - "Gérard G. Medioni"
doi: ""
url: "https://ijcai.org/proceedings/2015/485"
pdf: "https://ijcai.org/proceedings/2015/0485.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "3445-3451"
track: "Special Track on Machine Learning"
keywords:
---

# Intersecting Manifolds: Detection, Segmentation, and Labeling

Shay Deutsch, Gérard G. Medioni

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 3445-3451.

## Abstract

Solving multi-manifolds clustering problems that include delineating and resolving multiple intersections is a very challenging problem. In this paper we propose a novel procedure for clustering intersecting multi-manifolds and delineating junctions in high dimensional spaces. We propose to explicitly and directly resolve ambiguities near the intersections by using 2 properties: One is the position of the data points in the vicinity of the detected intersection; the other is the reliable estimation of the tangent spaces away from the intersections. We experiment with our method on a wide range of geometrically complex settings of convoluted intersecting manifolds, on which we demon- strate higher clustering performance than the state of the art. This includes tackling challenging geometric structures such as when the tangent spaces at the intersections points are not orthogonal.