Foreground Detection by Robust PCA solved via a Linearized Alternating Direction Method

Charles Guyon (1) , Thierry Bouwmans (1) , El-Hadi Zahzah (1)

1 MIA - Mathématiques, Image et Applications - EA 3165

Robust Principal Components Analysis (RPCA) shows a nice framework to separate moving objects from the background. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. RPCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the l1-norm. To solve this convex program, an Alternating Direction Method (ADM) is commonly used. However, the subproblems in ADM are easily solvable only when the linear mappings in the constraints are identities. This assumption is rarely verified in real application such as foreground detection. In this paper, we propose to use a Linearized Alternating Direction Method (LADM) with adaptive penalty to achieve RPCA for foreground detection. LADM alleviates the constraints of the original ADM with a faster convergence speed. Experimental results on different datasets show the pertinence of the proposed approach.

Mots clés: Background Modeling; Foreground Detection; RPCA

Domaines: Traitement des images [eess.IV]

Charles Guyon, Thierry Bouwmans, El-Hadi Zahzah. Foreground Detection by Robust PCA solved via a Linearized Alternating Direction Method. International Conference on Image Analysis and Recognition, ICIAR 2012, Jun 2012, Portugal. pp.115-122. ⟨hal-00809463⟩