Deformable kernels for early vision

By Pietro Perona. 1991

A technique is presented that allows (1) computing the best approximation of a given family using linear combinations of a small number of basis functions; and (2) describing all finite-dimensional families, i.e. the families of filters for which a finite-dimensional representation is possible with no error. The technique is general and can be applied to generating filters in arbitrary dimensions. Experimental results that demonstrate the applicability of the technique to generating multi-orientation multiscale 2-D edge-detection kernels are presented. The implementation issues are also discussed.<<ETX>>

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Citations in the corpus

Polar Transformer Networks (2017, methodology): “Exhaustive sampling for the creation of such a basis was proposed by [21] using the SVD.”
CubeNet: Equivariance to 3D Rotation and Translation (2018, methodology): “In this case, Perona [37] showed that he could approximate Equation 7 using an SVD formulation.”
A Unified Theory for Steerable and Quadrature Filters (2006, background): “The problem of approximating such a function by a smaller number of basis functions, allowing a certain error, has been examined in (Perona, 1995) and is not topic of this paper.”
Deformable Convolutional Networks (2017, background): “We note that although the term deformable kernels is used in [45], its meaning is different from ours in this work.”
Deep Convolutional Neural Network for Image Deconvolution (2014, background): “Kernel separability is achieved via singular value decomposition (SVD) [26] .”
Evaluation of Interest Point Detectors (2000, background): “This is con rmed by Perona [35] who has 28”
The Statistics of Natural Image (1998, methodology): “…is based upon measurement of the gradient of the intensity function using steerable rst derivative of Gaussian lters (Freeman & Adelson, 1991; Perona, 1995), and on estimation of the locations of zero-crossings of steerable second and third derivative of Gaussian lters, steered in the…”
Efficient deformable filter banks (1998, methodology): “Classical image processing problems (enhancement, denoising) may be approached successfully using elementary descriptors such as edges and textures.”
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space (2006, background): “Receptive fields of simple cells are modeled usually as convolution kernels of even and odd filters such as Gabor filters [12, 33, 42, 52].”
Spherical Tensor Calculus for Local Adaptive Filtering (2009, methodology): “Perona generalize d this concept in [8] and introduced a methodology to decompose a given filter kernel o ptimally in a set of steerable basis filters.”