Scale selection for differential operators [chapter]

Tony Lindeberg
1994 Scale-Space Theory in Computer Vision  
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds for a wide class of networks defined from linear and nonlinear differential expressions expressed in terms of scale-normalized scale-space derivatives. Then, we present a more detailed development of one example of such a network constructed from a
more » ... ed from a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of an oriented quasi quadrature combination of first-and second-order directional Gaussian derivatives, we couple such primitive computations in cascade over combinatorial expansions over image orientations. Scale-space properties of the computational primitives are analysed, and we give explicit proofs of how the resulting representation allows for scale and rotation covariance. A prototype application to texture analysis is developed, and it is demonstrated that a simplified mean-reduced representation of the resulting QuasiQuadNet leads to promising experimental results on three texture datasets.
doi:10.1007/978-1-4757-6465-9_13 fatcat:y5wwueoimzb4lixmk5i5wtaewi