The Fourier Transform and Its Applications
01 Aug 1966-American Journal of Physics (American Association of Physics Teachers)-Vol. 34, Iss: 8, pp 712-712
About: This article is published in American Journal of Physics.The article was published on 1966-08-01. It has received 2834 citations till now. The article focuses on the topics: Fourier transform.
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TL;DR: The theory of edge detection explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround ∇2G filters acting on the image forms the basis for a physiological model of simple cells.
Abstract: A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of delta 2G(x,y)*I(x,y) for image I, where G(x,y) is a two-dimensional Gaussian distribution and delta 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround delta 2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).
6,893 citations
16 Nov 1992
TL;DR: Optical coherence tomography (OCT) has developed rapidly since its first realisation in medicine and is currently an emerging technology in the diagnosis of skin disease as mentioned in this paper, where OCT is an interferometric technique that detects reflected and backscattered light from tissue.
Abstract: Optical coherence tomography (OCT) has developed rapidly since its first realisation in medicine and is currently an emerging technology in the diagnosis of skin disease. OCT is an interferometric technique that detects reflected and backscattered light from tissue and is often described as the optical analogue to ultrasound. The inherent safety of the technology allows for in vivo use of OCT in patients. The main strength of OCT is the depth resolution. In dermatology, most OCT research has turned on non-melanoma skin cancer (NMSC) and non-invasive monitoring of morphological changes in a number of skin diseases based on pattern recognition, and studies have found good agreement between OCT images and histopathological architecture. OCT has shown high accuracy in distinguishing lesions from normal skin, which is of great importance in identifying tumour borders or residual neoplastic tissue after therapy. The OCT images provide an advantageous combination of resolution and penetration depth, but specific studies of diagnostic sensitivity and specificity in dermatology are sparse. In order to improve OCT image quality and expand the potential of OCT, technical developments are necessary. It is suggested that the technology will be of particular interest to the routine follow-up of patients undergoing non-invasive therapy of malignant or premalignant keratinocyte tumours. It is speculated that the continued technological development can propel the method to a greater level of dermatological use.
6,095 citations
Book•
01 Feb 2006TL;DR: Wavelet analysis of finite energy signals and random variables and stochastic processes, analysis and synthesis of long memory processes, and the wavelet variance.
Abstract: 1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.
2,734 citations
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2,428 citations
TL;DR: A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible.
Abstract: A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture uses a network of Gaussian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibit by the nonlinear functions, the algorithm is proven to be globally stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with example systems. >
2,254 citations