Introduction to the Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and Analysis

©1998 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.1998.66117

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Model-Based Edge Detector for Spectral Imagery Using Sparse Spatiospectral Masks

Two model-based algorithms for edge detection in spectral imagery are developed that specifically target capturing intrinsic features such as isoluminant edges that are characterized by a jump in color but not in intensity. Given prior knowledge of the classes of reflectance or emittance spectra associated with candidate objects in a scene, a small set of spectral-band ratios, which most profoundly identify the edge between each pair of materials, are selected to define a edge signature. The bands that form the edge signature are fed into a spatial mask, producing a sparse joint spatiospectral nonlinear operator. The first algorithm achieves edge detection for every material pair by matching the response of the operator at every pixel with the edge signature for the pair of materials. The second algorithm is a classifier-enhanced extension of the first algorithm that adaptively accentuates distinctive features before applying the spatiospectral operator. Both algorithms are extensively verified using spectral imagery from the airborne hyperspectral imager and from a dots-in-a-well midinfrared imager. In both cases, the multicolor gradient (MCG) and the hyperspectral/spatial detection of edges (HySPADE) edge detectors are used as a benchmark for comparison. The results demonstrate that the proposed algorithms outperform the MCG and HySPADE edge detectors in accuracy, especially when isoluminant edges are present. By requiring only a few bands as input to the spatiospectral operator, the algorithms enable significant levels of data compression in band selection. In the presented examples, the required operations per pixel are reduced by a factor of 71 with respect to those required by the MCG edge detector

Fuzzy geometry, entropy, and image information

Presented here are various uncertainty measures arising from grayness ambiguity and spatial ambiguity in an image, and their possible applications as image information measures. Definitions are given of an image in the light of fuzzy set theory, and of information measures and tools relevant for processing/analysis e.g., fuzzy geometrical properties, correlation, bound functions and entropy measures. Also given is a formulation of algorithms along with management of uncertainties for segmentation and object extraction, and edge detection. The output obtained here is both fuzzy and nonfuzzy. Ambiguity in evaluation and assessment of membership function are also described

Fuzzy logic-based approach to wavelet denoising of 3D images produced by time-of-flight cameras

In this paper we present a new denoising method for the depth images of a 3D imaging sensor, based on the time-of-flight principle. We propose novel ways to use luminance-like information produced by a time-of flight camera along with depth images. Firstly, we propose a wavelet-based method for estimating the noise level in depth images, using luminance information. The underlying idea is that luminance carries information about the power of the optical signal reflected from the scene and is hence related to the signal-to-noise ratio for every pixel within the depth image. In this way, we can efficiently solve the difficult problem of estimating the non-stationary noise within the depth images. Secondly, we use luminance information to better restore object boundaries masked with noise in the depth images. Information from luminance images is introduced into the estimation formula through the use of fuzzy membership functions. In particular, we take the correlation between the measured depth and luminance into account, and the fact that edges (object boundaries) present in the depth image are likely to occur in the luminance image as well. The results on real 3D images show a significant improvement over the state-of-the-art in the field. (C) 2010 Optical Society of Americ