Factor Graphs for Computer Vision and Image Processing

Factor graphs have been used extensively in the decoding of error correcting codes such as turbo codes, and in signal processing. However, while computer vision and pattern recognition are awash with graphical model usage, it is some-what surprising that factor graphs are still somewhat under-researched in these communities. This is surprising because factor graphs naturally generalise both Markov random fields and Bayesian networks. Moreover, they are useful in modelling relationships between variables that are not necessarily probabilistic and allow for efficient marginalisation via a sum-product of probabilities. In this thesis, we present and illustrate the utility of factor graphs in the vision community through some of the field’s popular problems. The thesis does so with a particular focus on maximum a posteriori (MAP) inference in graphical structures with layers. To this end, we are able to break-down complex problems into factored representations and more computationally realisable constructions. Firstly, we present a sum-product framework that uses the explicit factorisation in local subgraphs from the partitioned factor graph of a layered structure to perform inference. This provides an efficient method to perform inference since exact inference is attainable in the resulting local subtrees. Secondly, we extend this framework to the entire graphical structure without partitioning, and discuss preliminary ways to combine outputs from a multilevel construction. Lastly, we further our endeavour to combine evidence from different methods through a simplicial spanning tree reparameterisation of the factor graph in a way that ensures consistency, to produce an ensembled and improved result. Throughout the thesis, the underlying feature we make use of is to enforce adjacency constraints using Delaunay triangulations computed by adding points dynamically, or using a convex hull algorithm. The adjacency relationships from Delaunay triangulations aid the factor graph approaches in this thesis to be both efficient and competitive for computer vision tasks. This is because of the low treewidth they provide in local subgraphs, as well as the reparameterised interpretation of the graph they form through the spanning tree of simplexes. While exact inference is known to be intractable for junction trees obtained from the loopy graphs in computer vision, in this thesis we are able to effect exact inference on our spanning tree of simplexes. More importantly, the approaches presented here are not restricted to the computer vision and image processing fields, but are extendable to more general applications that involve distributed computations

PLATFORM REEF LAGOON DETECTION FROM SENTINEL-2 IN PANGGANG ISLAND AND SEMAKDAUN ISLAND

Processing of satellite image data for the detection of platform reef lagoons is intended as one of the geo-physical parameters of the reef landform. Panggang Island and Semakdaun Island were chosen to make the detection model because they are ideal for lagoon reef landforms and tapulang court reefs. This model is only valid in the continental shelf area and the back arc and small island tectonic type. Determination of this location is done to improve the accuracy of spectral-based data processing. Platform reefs are one of four classes of reef landforms. Sentinel-2A data with a spatial resolution of 10m, blue, green, red, and near infrared bands were selected to investigate their ability to detect lagoons. Processing of data by calculating the Optimum Index Factor (OIF) to produce a composite image and drawing transect lines to produce pixel values and spectral graphics of the lagoon. The results of data processing in the form of graphs, composite images and pixel values were built to realize a digital lagoon detection model. These results are used for lagoon growth stage analysis for the classification of three reef platform landforms, visually and digitally interpretation. This digital and visual detection system design is useful for monitoring coral reef ecosystems

Towards Building Deep Networks with Bayesian Factor Graphs

We propose a Multi-Layer Network based on the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional lattice. The Latent Variable Model (LVM) is the basic building block of a quadtree hierarchy built on top of a bottom layer of random variables that represent pixels of an image, a feature map, or more generally a collection of spatially distributed discrete variables. The multi-layer architecture implements a hierarchical data representation that, via belief propagation, can be used for learning and inference. Typical uses are pattern completion, correction and classification. The FGrn paradigm provides great flexibility and modularity and appears as a promising candidate for building deep networks: the system can be easily extended by introducing new and different (in cardinality and in type) variables. Prior knowledge, or supervised information, can be introduced at different scales. The FGrn paradigm provides a handy way for building all kinds of architectures by interconnecting only three types of units: Single Input Single Output (SISO) blocks, Sources and Replicators. The network is designed like a circuit diagram and the belief messages flow bidirectionally in the whole system. The learning algorithms operate only locally within each block. The framework is demonstrated in this paper in a three-layer structure applied to images extracted from a standard data set.Comment: Submitted for journal publicatio

Signal Flow Graph Approach to Efficient DST I-IV Algorithms

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having $(n-1)$ points signal flow graph for DST-I and $n$ points signal flow graphs for DST II-IV

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

Design of multimedia processor based on metric computation

Media-processing applications, such as signal processing, 2D and 3D graphics rendering, and image compression, are the dominant workloads in many embedded systems today. The real-time constraints of those media applications have taxing demands on today's processor performances with low cost, low power and reduced design delay. To satisfy those challenges, a fast and efficient strategy consists in upgrading a low cost general purpose processor core. This approach is based on the personalization of a general RISC processor core according the target multimedia application requirements. Thus, if the extra cost is justified, the general purpose processor GPP core can be enforced with instruction level coprocessors, coarse grain dedicated hardware, ad hoc memories or new GPP cores. In this way the final design solution is tailored to the application requirements. The proposed approach is based on three main steps: the first one is the analysis of the targeted application using efficient metrics. The second step is the selection of the appropriate architecture template according to the first step results and recommendations. The third step is the architecture generation. This approach is experimented using various image and video algorithms showing its feasibility