【 Kernel function 】 A kernel function is a function k that for all x, z ∈ X satisfies where is a mapping from X to an (inner product) feature space F
The computation of a scalar product between two feature space vectors, can be readily reformulated in terms of a kernel function k
Is necessary? Not necessary What kind of k can be used? symmetric positive semi-definite ( kernel matrix ) Given a feature mapping, caan we compute the inner product in feature space? Yes Given a kernel function k, whether a feature mapping is existence? Yes [Mercer’s theorem]
Feature correspondences can be used to construct an image comparison kernel that is appropriate for SVM-based classification, and often outperforms BOFs. Image representations that enforce some degree of spatial consistency usually perform better in image classification tasks than pure bags of features that discard all spatial information.
We need to design a good image similarity measure: ≈ ?
Graph-matching Method in this paper Sparse Features NN Classifier Slow Use pair-wise Information Lower performance As Dense SVM Classifier Fast enough Use pair-wise Information State-of-the-art performance
An image I = a graph G = Nodes + Edges A node n=d n (x n,y n ) represent a region of I, Each region is represented by a image Feature vector F n,e.g. SIFT....
Matching two iamges is realized by maximizing the energy function: