Paper Info
Title
A Mumford Shah Style Unified Framework For Layering: Pitfalls And Solutions
Abstract
Layered models are commonly used in computer vision to estimate the shape, appearance, depth ordering, occlusion structure and motion of objects from a set of images, offering computationally simpler alternatives to full 3D scene models. A unified computational framework for the various modeling elements (shape, appearance, motion and depth ordering), which integrates much of the current and prior work on layered models, would aid our understanding and development of layer extraction algorithms. A notable earlier work by Jackson et al. [2008] sought to provide such a framework in the context of variational methods, neatly cast as a single joint optimization problem. However, it did not perform as anticipated and has not been further developed. As the complexity of their formulation may have hindered its continued exploration, we reformulate their diffeomorphic approach within the much simpler framework of active contours. More importantly, though, we uncover a tricky modeling flaw which poorly extended the classical Mumford-Shah segmentation model to layering, causing unexpected performance degradation of their potentially powerful formulation. We elucidate this flaw and demonstrate its unintended consequences (a shrinking effect on foreground layers). We fix this problem by abandoning their unconstrained joint optimization philosophy and implementing an augmented Lagrangian style optimization process with PDE constraints instead. This new approach, which splits the classical Mumford-Shah appearance and geometric priors into two separate cost functions (one to be minimized with the other as a constraint) fixes the unintended shrinking problem and more properly extends the Mumford-Shah modeling paradigm into the layered framework, yielding far superior results. In doing so, we establish a more solid mathematical foundation for a unified variational approach to layering.
Year
DOI
Venue
2018
10.1007/978-3-030-03801-4_31
ADVANCES IN VISUAL COMPUTING, ISVC 2018
Keywords
Field
DocType
Layered models, Active contours, Mumford-Shah, PDEs
Computer vision,Segmentation,Computer science,Algorithm,Layering,Augmented Lagrangian method,Artificial intelligence,Prior probability,Optimization problem,Diffeomorphism
Conference
Volume
ISSN
Citations 
11241
0302-9743
0
PageRank 
References 
Authors
0.34
16
3
Name
Order
Citations
PageRank
Fareed ud din Mehmood Jafri100.34
Martin Mueller2121.41
Anthony J. Yezzi32016151.48