Discrete Inference and Learning in Artificial Vision

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Artificialvision applications, such as object detection in natural images and automaticsegmentation of medical acquisitions, rely on models that interpret the visualinformation provided to a computer. The model provides a compromise between thesupport given by the observations and the prior domain knowledge. This courseis concerned with the two computational problems that arise when using such modelsin practice.

Inference(Energy Minimization):

Given a visual observation (for example, an image or an MRI scan), weare interested in estimating its most likely interpretation (i.e. the location of allthe objects in the image, or the segments of the MRI scan) according to themodel. While the problem cannot be solved optimally, we will describe state of the art approximate algorithms that provide very accurate solutions inpractice. While the theoretical properties of the algorithms will be discussedbriefly, the main emphasis will be on their application.

 Learning(Parameter Estimation):

Given a set of training samples consisting of inputs and their desiredoutputs, (for example, images and the location of the objects, or MRI scans andtheir segmentations) we would like to estimate a model that is suited to thetask at hand. We will show how the problem of learning a model can beformulated as empirical risk minimization. Furthermore, we will presentefficient algorithms for solving the corresponding optimization problem.

• Lecture1: Introduction to artificial vision with discrete graphical models: In this lecture, the interdisciplinary nature ofcomputational vision is briefly introduced along with its potential use indifferent application domains. Subsequently, the concept of discrete modelingof artificial vision tasks is introduced from theoretical view point along withshort examples demonstrating the interest of such an approach in low, mid andhigh-level vision. Examples refer to blind image deconvolution, knowledge-basedimage segmentation, optical flow, graph matching, 2d-to-3d view-point invariantdetection and modeling and grammar-driven image based reconstruction.
• Lecture2: Reparameterization and dynamic programming: In this lecture, we provide a brief introduction toundirected graphical models. We also provide a formal definition of the problemof inference (specifically, energy minimization). We introduce the concept ofreparameterization, which forms the building block of all the inferencealgorithms discussed in the course. We describe a simple inference algorithmknown as dynamic programming, which consists of a series of reparameterization.We show how dynamic programming can be used to perform exact inference onchains.
  
• Lecture3: Maximum flow and minimum cut:  In this lecture, we introduce the concept of functions on arcs of a directed graph. Wefocus on a special function known as the flow function. Associated with thisfunction is the combinatorial optimization problem of computing the maximumflow of a directed graph. We also introduce the concept of a cut in a directedgraph, and prove that the minimum cost cut is equivalent to the maximum flow.We describe a simple algorithm for solving the maximum flow, or equivalent theminimum cut, problem.
• Lecture4: Minimum cut based inference: In this lecture, we show how the problem of inference for undirectedgraphical models with two labels can be formulated as a minimum cut problem. Wecharacterize the energy function that can be minimized optimally using theminimum cut problem. We show examples using the image segmentation and texturesynthesis problems, which can be formulated using two labels. We consider themulti-label problem, and devise approximate algorithms for inference based onthe minimum cut algorithms. We show examples using the stereo reconstructionand the image denoising problems.
  
• Lecture5: Belief propagation: In this lecture we present the basic concepts ofmessage passing and belief propagation networks. The concept is initiallydemonstrated using chains, extended to the case of trees and then eventually toarbitrary graphs. The strengths and the limitations of such an optimizationframework are presented. The image completion and texture synthesis problemsare considered as examples to demonstrate the interest of such a family ofoptimization algorithms.
  
• Lecture6: Linear programing and duality:  In this lecture, discrete inference is addressed through concepts comingfrom linear programming relaxations. In particular, we explain how agraph-optimization problem can be expressed as a linear programing one and thenhow one can take benefit of the duality theorem to develop efficientoptimization methods. The problem of optical flow and its deformableregistration variant in medical image analysis is considered as an example todemonstrate the interest of such optimization algorithms.
• Lecture7: Dual decomposition and higher order graphs: In this lecture, we introduce the dual decompositionframework for the optimization of low rank and higher order graphical models.First, we demonstrate the concept of the method using a simple toy example andthen we extend to the most general optimization problem case. Three differentexamples are considered in the context of higher order optimization, theproblem of linear mapping between images, the case of dense deformable graphmatching and the development of pose invariant object segmentation methods inthe context of medical imaging.
  
• Lecture 8: Parameter learning: In this lecture, we introduce two frameworks for estimating the parametersof a graphical model using fully supervised training data. The first frameworkmaximizes the likelihood of the training data while regularizing theparameters. The second framework minimizes the empirical risk, as measured by auser-defined loss function, while regularizing the parameters. We provide abrief description of the algorithms required to solve the related optimizationproblems. We show the results obtained on standard machine learningdatasets.