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Complex Networks for Representation and Characterization of Images. For CS790g Project Bingdong Li 9/23/2009. Outline. Background Motivation Current States (CS): Representation Characterization Using examples from Backes, Casanova, and Bruno’s Approach using local information
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Complex Networks for Representation and Characterization of Images For CS790g Project Bingdong Li 9/23/2009
Outline Background Motivation Current States (CS): Representation Characterization Using examples from Backes, Casanova, and Bruno’s Approach using local information Kim, Faloutsos and Hebert’s Approach using global information Comparison of Two Approaches Summary Questions and Comments
Background: Complex Network Source: cs790: complex network lecture
Background: Image Source: CS674 Image Processing Lecture
Background: Image Processing Source: CS674 Image Processing Lecture
Background: Image Representation Source: CS674 Image Processing Lecture
Outline Background Motivation
Motivation Belief: Computer vision is one of the most difficult problem remains, how can we represent and characterize image in the way of complex network so that we analysis it? For a given problem, if it can be described in the way of mathematics, it is half way to solve the problem.
Outline Background Motivation Current States (CS): Representation Characterization Using examples from Backes, Casanova, and Bruno’s Approach using local information
CS: Backes’ Approach • Construction of graph, • Vertices: points of shape boundary are modeled as fully connected network, • Weight: the Euclidean distance d • through a sequential thresholds Tl (d< Tl), the fully connected network becomes a dynamic complex network, the topological features of the growth of the dynamic network are used as a shape descriptor (or signature)
CS: Backes’ Approach • Properties of the complex network • High clustering coefficient • The small world property
CS: Backes’ Approach • Dynamic evolution signature • F: T T where Tini and TQ, respectively, the initial and final threshold
CS: Backes’ Approach • Characterization • Degree descriptor kμ average degree, Kk max degree
CS: Backes’ Approach • Evolution by a threshold T=0.1, .15, .20
CS: Backes’ Approach Process of extraction of degree descriptor from an Image
CS: Backes’ Approach • Advantage of Degree Descriptors • Rotation and scale inveriance • Noise tolerance • Robustness
CS: Backes’ Approach Representation of rotate invariance
CS: Backes’ Approach Representation of scale invariance
CS: Backes’ Approach • Characterization • Joint Degree descriptor Is the concatenation of the entropy(H), energy(E), and average joint degree(P) at each instant threshold T
CS: Backes’ Approach • Advantage of Joint Degree Descriptors • Rotation and scale inveriance • Noise tolerance • Robustness • Normalization of vertex is irrelevant because the joint degree concerns the probability distribution P(ki,k’)i
CS: Backes’ Approach • Weakness of Backe’s Approach: • Initial and final threshold
Outline Background Motivation Current States (CS): Representation Characterization Using examples from Backes, Casanova, and Bruno’s Approach using local information Kim, Faloutsos and Hebert’s Approach using global information
CS: Kim’s Approach Construct Visual Similarity Network (VSN) Vertices (V): features of from training images Edges (E): link features that matched across images Weights (W): consistence of correspondence with all other correspondences in matching image Ia and Ib VSN = (V, E, W)
CS: Kim’s Approach Construction of VSN Vertices: can be any unit of local visual information. In this approach, features detected using Harris-Affine point detector and the SIFT descriptor
CS: Kim’s Approach Construction of VSN Edges: established between features in different images. Spectral matching algorithm is used to each pair of image (Ia, Ib) A new edge is established between feature ai and bj
CS: Kim’s Approach Construction of VSN Edge weights M n*n is a spare weight matrix, M(ai , bj) is the weight value
CS: Kim’s Approach Characterization Ranking of information Remove noisy Measure the importance P is the PageRank vector
CS: Kim’s Approach Characterization Structural similarity “similar nodes are highly likely to exhibit similar link structures in the graph” p.4 The similarity is computed by using link analysis algorithm
CS: Kim’s Approach Characterization Link analysis algorithm Given a VSN G, a node ai , the neighborhood subgraph Gai either pointed to ai or point to by ai M, the adjacency matrix of G ai.
CS: Kim’s Approach The left image is extracted features, the right image shows top20% high-ranked features
CS: Kim’s Approach Weakness of Kim’s Approach Using threshold in computing edge weights Mystery constant α =0.1 Category partition to pre-determined K groups The difference of objects appearance in the training data set is too big, make the conclusion weak
Outline Background Motivation Current States (CS): Comparison of Two Approaches
Comparison • Backes’s Approach • Unsupervised approach • using local information • Dynamic complex network • More task on complex network, less work on image processing • Kim’s Approach • Supervised approach • using global information • Static complex network • More work on image processing, less work on complex network • Both using threshold, but Backe’s approach based on initial and final value,
Outline Background Motivation Current States (CS): Comparison of Two Approaches Summary
Summary • In both approaches using complex network for representation and characterization of image, • provide a unique way for object classification and analysis, • present better results than traditional and state-of-art methods, • demonstrate the potential of complex network analysis to computer vision.
