Oriented filters are useful in many early vision and image processing tasks. One often needs to apply the same filter, rotated to different angles under adaptive control, or wishes to calculate the filter response at various orientations. We present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively "steer" a filter to any orientation, and to determine analytically the filter output as a function of orientation.

Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be considered in the context of other domains, particularly orientation and scale. We explore "jointly shiftable" transforms that are simultaneously shiftable in more than one domain. Two examples of jointly shiftable transforms are designed and implemented: a one-dimensional tran...

Two paradigms for visual analysis are top-down, starting from high-level models or information about the image, and bottom-up, where little is assumed about the image or objects in it. We explore a local, bottom-up approach to image analysis. We develop operators to identify and classify image junctions, whichcontain important visual cues for identifying occlusion, transparency, and surface bends. Like the human visual system, we begin with the application of linear filters which are oriented in all possible directions. Wedevelop an efficientway to create an oriented filter of arbitrary orientation by describing it as a linear combination of basis filters. This approach to oriented filtering, which we call steerable filters, offers advantages for analysis as well as computation. We design a variety of steerable filters, including steerable quadrature pairs, which measure local energy. We show applications of these filters in orientation and texture analysis, and image representation and enhanc...

Abstract—Receptive � elds of simple cells in the primate visual cortex were well � t in the space and time domains by the Gaussian Derivative (GD) model for spatio-temporal vision. All 23 � elds in the data sample could be � t by one equation, varying only a single shape number and nine geometric transformation parameters. A difference-of-offset-Gaussians (DOOG) mechanism for the GD model also � t the data well. Other models tested did not � t the data as well as or as succinctly, or failed to converge on a unique solution, indicatingover-parameterization.An ef � cient computationalalgorithm was found for the GD model which produced robust estimates of the direction and speed of moving objects in real scenes. 1.

This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. Estimation of depth from the blur difference is straightforward. The algorithm is based on a local image decomposition technique using the Hermite polynomial basis. We show that any coefficient of the Hermite polynomial computed using the more blurred image is a function of the partial derivatives of the other image and the blur difference. Hence, the blur difference can be computed by resolving a system of equations. All computations required are local and carried out in the spatial domain. An algorithm is presented for estimation of the blur in 1D and 2D cases and its behavior is studied for constant images, step edges, line edges and junctions. The algorithm is tested using synthetic and real images. The results obtained are very encouraging. 1 Introd...

closely related, often differing only by a linear transformation. Consider the problem of matching an observed local image intensity pattern against a set of candidate patterns. A brute-force solution, in which one rotates the image pattern through a set of discretized orientations searching for an optimal match is inelegant, inefficient, and highly susceptible to local minima. A number of authors have taken the approach of first estimating a "dominant" orientation from the projection onto loworder basis functions (e.g., the gradient), and using this estimate to align the two patterns for comparison (e.g., [7, 14, 15, 16, 5]). This type of approach, while efficient, becomes unstable for patterns lacking a Research partially supported by an NSF CAREER grant to EPS. strongly dominant orientation. More generally, one can use the theory of algebraic invariants to construct rotation-invariant representations of image content [1, 12, 13, 14]. The theory allows one to constr

This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. Estimation of depth from the blur difference is straightforward. The algorithm is based on a local image decomposition technique using the Hermite polynomial basis. We show that any coecient of the Hermite polynomial computed using the more blurred image is a function of the partial derivatives of the other image and the blur dierence. Hence, the blur difference is computed by resolving a system of equations. The resulting estimation is dense and involves simple local operations carried out in the spatial domain. The mathematical developments underlying estimation of the blur in both 1D and 2D images are presented. The behavior of the algorithm is studied for constant images, step edges, line edges and junctions. The selection of its parameters is discussed...

New method to eliminate block artifact in high compressed images is presented. Here the emphasis is placed on Hermite transform and we also accentuate on pixel near the block boundaries, and, because it is a polynomial transform with a gaussian window that is in a good agreement with human visual processing procedure.

This work is intended to provide some ideas on the use of a Gaussian-derivative model for visual perception, called the Hermite transform, to extract motion information from an image sequence. Gaussian-derivative operators have long been used in computer vision for feature extraction and are relevant in visual system modeling. A directional energy is defined in terms of the 1-D Hermite transform coefficients of local projections. Each projection is described by the Hermite transform, resulting in a directional derivative analysis of the input at a given spatiotemporal scale. We demonstrate that the 1-D Hermite transform coefficients of local projections are readily computed as a linear mapping of the 3-D Hermite transform coefficients through some projecting functions. The directional response is used to detect spatiotemporal patterns that are 1-D or 2-D. Practical consideration and experimental results are also of concern.

In this work, a multi-channel model for image representation is derived based on the scale-space theory. This model is inspired in biological insights and includes some important properties of human vision such as the Gaussian derivative model for early vision proposed by Young. 25 The image transform that we propose in this work uses analysis operators similar to those of the Hermite transform at multiple scales, but the synthesis scheme of our approach integrates the responses of all channels at different scales. The advantages of this scheme are: 1) both analysis and synthesis operators are Gaussian derivatives. This allows for simplicity during implementation. 2) The operator functions possess better space-frequency localization, and it is possible to separate adjacent scales one octave apart, according to Wilson’s results on human vision channels. 22 3) In the case of 2-D signals, it is easy to analyze local orientations at different scales. A discrete approximation is also derived from an asymptotic relation between the Gaussian derivatives and the discrete binomial filters. We show in this work how the proposed transform can be applied to the problems of image coding, noise reduction and image fusion. Practical considerations are also of concern.