Steerable Wavelet Machines (SWM): Learning Moving Frames for Texture Classification
Adrien Depeursinge, Emmanuel Soubies, EPFL STI LIB

Meeting • 03 May 2016 • BM 4 233

Abstract
Title 1: Steerable Wavelet Machines (SWM): Learning Moving Frames for Texture Classification Presenter 1: Adrien Abstract 1: We present texture operators encoding class-specific local organizations of image directions (LOID) in a rotation-invariant fashion. The LOIDs are key for visual understanding, and are at the origin of the success of the popular approaches such as local binary patterns (LBP) and the scale-invariant feature transform (SIFT). Whereas LBPs and SIFT yield handcrafted image representations, we propose to learn data-specific representations of the LOIDs in a rotation-invariant fashion. The image operators are based on steerable circular harmonic wavelets (CHW), offering a rich and yet compact initial representation for characterizing natural textures. The joint location and orientation required to encode the LOIDs is preserved by using moving frames (MF) texture representations built from locally-steered multi-order CHWs. In a second step, we use support vector machines (SVM) to learn a multi-class shaping matrix of the initial CHW representation, yielding data-driven MFs that are invariant to rigid motions. We experimentally demonstrate the effectiveness of the proposed operators for classifying natural textures. Title 2: Some results on MA-TIRF reconstruction and exact continuous penalties for l2-l0 minimization Presenter 2: Emmanuel Soubies Abstract 2: In the first part of this presentation, I will present some work related to Multi-Angle Total Internal Reflection Fluorescence (MA-TIRF) reconstruction. This microscopy technique is a method of choice to visualize membrane-substrate interactions. After an introduction on TIRF microscopy, I will present microscope calibration techniques which are essential for the success of reconstruction methods. Then, I will roughly introduce the reconstruction methods that can be used to solve the ill-posed inverse problem allowing to compute a quantitative depth map with high axial resolution. Finally, biological reconstructions on real samples will be presented. In a second time, I will focus on sparse approximation and more precisely on nonconvex continuous penalties approximating the l0-pseudo norm within the framework of the l0-regularized least squares problem. I will introduce the Continuous Exact l0 penalty (CEL0), an approximation of the l0-norm leading to a tight continuous relaxation of the l2-l0 criteria. Relationships between minimizers of the initial and relaxed functionals will be presented showing that the CEL0 functional provides an equivalent continuous reformulation of the l2–l0 objective. Thanks to the continuity of this relaxation, recent nonsmooth nonconvex algorithms can be used to address its minimization. Finally, applications in signal processing will be presented and an unification on such continuous exact relaxations will be shortly commented.