Phillip E Sheridan

A Method to Perform a Fast Fourier Transform With Primitive Image Transformations

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC

Generalization of learning by synchronous waves: from perceptual organization to invariant organization

From a few presentations of an object, perceptual systems are able to extract invariant properties such that novel presentations are immediately recognized. This may be enabled by inferring the set of all representations equivalent under certain transformations. We implemented this principle in a neurodynamic model that stores activity patterns representing transformed versions of the same object in a distributed fashion within maps, such that translation across the map corresponds to the relevant transformation. When a pattern on the map is activated, this causes activity to spread out as a wave across the map, activating all the transformed versions represented. Computational studies illustrate the efficacy of the proposed mechanism. The model rapidly learns and successfully recognizes rotated and scaled versions of a visual representation from a few prior presentations. For topographical maps such as primary visual cortex, the mechanism simultaneously represents identity and variation of visual percepts whose features change through time.

Cortical Specification of a Fast Fourier Transform Supports a Convolution Model of Visual Perception

Currently, the full extent of the role Fourier analysis plays in biological vision is unclear. Although we have examples of sensory organs that perform Fourier transforms, e.g. the lens of the eye and the cochlear, to date there is no direct empirical evidence for its implementation in cortical architecture. However, there does exist intriguing theoretical evidence that suggests a role for the Fourier transform in a primate’s primary visual cortex (area V1) which emerges from recent developments in our knowledge of contextual modulation. This paper proposes a new Fourier transform and a specification of how this transform has a natural implementation in cortical architecture. The significance of this new Fourier transform and its specification in neural circuitry is that it provides a plausible explanation for previously unexplained observable properties of the primate vision system.

Contextual modulation via low-level vision processing

Gabor wavelets are well established as being useful for modeling neuronal response properties of the primary visual cortex. However, current Gabor models do not account for long-range contextual modulation. This paper introduces a new model which extends a state-of-the-art model of contextual modulation by incorporating long-range convolution at the scale of the visual field. The significance of this new mechanism is that it accounts for perceptual filling-in of occluded receptive fields with purely low-level vision processing.

Fast Fourier transform in the spiral honeycomb image algebra

The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes one such efficient implementation and discusses its implications to digital technology as well as biological vision. The significance of the fast Fourier transform (FFT) presented in this paper is that it provides geometrical meaning to the regrouping of a Cooley-Tukey type FFT.

Collaborative Supervision of Machine Learning as a Tool for Web-Based Education: A Teaching and Learning Triangle

Machine-learning applications often suffer bottlenecks due to inefficiency in the human-machine interface. A novel architecture design has been developed to allow expert supervisors to collaborate and cooperate in real-time to alleviate the effects of the bottleneck. Replacing supervisors with students, this architecture also allows for supervised training and collaborative learning of students as well as machine learners. Our attempts to provide Web-based courses to distance learners have highlighted the need for more effective use of the medium for education and appropriate tools to provide the necessary richness of experience. We present our design and an example application to demonstrate how we address some of the shortfalls present in Web-based, distance education.

Collaborative supervision of machine vision systems: Breaking a sequential bottleneck in the supervised learning process

This paper describes a computer vision system in the context of exploiting parallelism. The key contribution is a description of a network design that breaks a long-standing bottleneck in the supervision phase of the vision process. The proposed solution draws from and contributes to the disciplines of machine learning, computer vision and collaborative editing. The significance of the solution is that it provides the means by which complex visual tasks such as mammography can be learned by an artificial vision system.