Michael P. Beddoes

Multiply sectioned Bayesian networks and junction forests for large knowledge-based systems

Bayesian networks provide a natural, concise knowledge representation method for building knowledge‐based systems under uncertainty. We consider domains representable by general but sparse networks and characterized by incremental evidence where the probabilistic knowledge can be captured once and used for multiple cases. Current Bayesian net representations do not consider structure in the domain and lump all variables into a homogeneous network. In practice, one often directs attention to only part of the network within a period of time; i.e., there is “localization” of queries and evidence. In such case, propagating evidence through a homogeneous network is inefficient since the entire network has to be updated each time. This paper derives reasonable constraints, which can often be easily satisfied, that enable a natural {localization preserving) partition of a domain and its representation by separate Bayesian subnets. The subnets are transformed into a set of permanent junction trees such that evidential reasoning takes place at only one of them at a time; and marginal probabilities obtained are identical to those that would be obtained from the homogeneous network. We show how to swap in a new junction tree, and absorb previously acquired evidence. Although the overall system can be large, computational requirements are governed by the size of one junction tree.

Optimal Edge Detector Design I: Parameter Selection and Noise Effects

This paper comments on the optimality of the Laplacian of a Gaussian edge detection filter which localizes edges through zero crossings in the filtered image. The arguments of both Marr and Hildreth, and Dickey and Shanmugam are reviewed to establish that the filter is optimal in the sense of maximizing output image energy near edge features. This filters principal advantage over other edge detectors is that its response is user-adjustable through selection of a single parameter, the Gaussian standard deviation. However, no clear method for the selection of this parameter has been provided. The problem is addressed here by applying the filter to two ideal periodic edge models blurred by a Gaussian distribution point-spread function. The observed response to the edge spacing and blur standard deviation is then translated into a filter parameter design procedure. The problems of optimum filter performance in the presence of additive Gaussian noise are then addressed. The problem of selecting the sampled filters coefficient word size is dealt with in a companion paper.

Paper: Multiply sectioned Bayesian networks for neuromuscular diagnosis

A prototype neuromuscular diagnostic system (PAINULIM) that diagnoses painful or impaired upper limbs has been developed based on Bayesian networks. This paper presents nonmathematically the major knowledge representation issues that arose in the development of PAINULIM. Motivated by the computational overhead of large application domains, and the desire to provide a user with an interface that gives a focused display of a subdomain of current interest, we built PAINULIM using the idea of multiply sectioned Bayesian networks. A preliminary evaluation of PAINULIM with 76 patients has demonstrated good clinical performance.

Optimal Edge Detector Design II: Coefficient Quantization

A companion paper describes the design and implementation of the Laplacian of a Gaussian edge detection filter which localizes edges through zero crossings in the filtered image. Accuracy in the presence of noise has been found to be proportional to the square root of the filters standard deviation. Digital implementation of any continuous filter requires sampling and coefficient quantization. The sampled filter was examined, but a method is proposed here for selection of a minimum coefficient word size for direct-form implementation to satisfy in-band rejection bounds.

A New Method for Obtaining Accurate Estimates of Vocal-Tract Filters and Glottal Waves From Vowel Sounds

Previously, estimating vocal-tract filters and glottal waves from vowel sounds imposed either the invalid assumption that glottal waves over closed glottal intervals are zero, or parametric models for glottal waves, resulting in biased vocal-tract-filter estimates and glottal-wave estimates lacking information over closed glottal intervals. We obtain unbiased vocal-tract-filter estimates from sustained vowel sounds, for which the glottal waveforms are periodically stationary random processes. Two equations are constructed each relating the vocal-tract filter to the sound signal and the glottal wave over one of two closed glottal intervals. By subtracting one equation from the other, the periodic components of the glottal wave are eliminated from the vocal-tract-filter estimation, and an unbiased vocal-tract-filter estimate is obtained. The average of many such estimates from different closed glottal intervals of the sound is the final estimate, which is used to obtain the glottal wave by inverse filtering the sound. The results obtained from vowel sounds /a/ produced by some subjects are presented. Over closed glottal phases, the glottal waves obtained are nonzero. During vocal-fold colliding, they increase; during vocal-fold parting, they decrease or even increase. The vocal-tract filters obtained yield vocal-tract area functions similar to that measured from an unknown subjects magnetic resonance image.

Fast binary-image boundary extraction

Abstract A scheme for obtaining boundaries of binary images is presented. It was inspired by Zahn. In 1969 he showed how to obtain outlines from a raster scanned binary image using a 3 × 2 pixel operator. The present proposal uses a slightly larger operator; it will produce complete descriptions of all closed borders (borders which encounter the outer edges of image space are not included). A nice feature is that only two of the most recently scanned lines of picture must be stored at any one time. Boundaries are continuously calculated during the scan; lookup tables and lists log and link the border points. It is important to signal when a closed contour has been detected. A very fast new, but not infallible, technique based on Euler numbers is proposed. Indication of closure is not guaranteed but it can be used to trigger slow-acting closure verification resulting in reduced processing overhead. Implementation design topics are illustrated in a number of simulations involving segmentation of 50 random-noise images. The results show that the real-time constraint can be satisfied with current technology when the natural parallelism within the system is exploited.

Discrimination of vowel sounds of very short duration

An experiment was conducted to investigate the discrimination of six vowel sounds of 10 msec duration. Vowels of equal pitch and intensity level were generated by computer. Both phonetically trained (PT) and untrained (UPT) Ss were used. Rapid learning took place, and the PT Ss showed much better discrimination than the UPT Ss. Confusion matrices of the last four learning blocks indicated that /i/ and /u/ sounded very much alike when they were short. The pattern of the test scores was discussed with reference to pure tone perception.

The silent interval of stop consonants.

An experiment was conducted to measure the silent interval (SI) preceding the burst of all the stop consonants in English. A list of words was constructed for each pair of stop cognates. More commonly used words with stop cognates in similar environments were chosen for the experiment. Six subjects spoke these lists and their speech samples were analysed with the aid of a digital computer and a precision display unit. The average durations of the SI found in descending order were: /p/, 117.64 msec; /k/, 113.09 msec; /t/, 102.04 msec; /b/, 85.58 msec; /g/, 79.97 msec, and /d/, 68.59 msec. The average difference in SI between the voiceless and voiced stop. cognates was about 33 msec. and the average ratio between them was about 1.4. By taking a variety of environments into consideration, the analysis of the SI yielded a result which suggests that the duration of the SI is strongly influenced by different phonetic environments: when homorganic nasal phonemes preceded, the SI was short; when short vowels preceded, the SI was long; when there was a stress pattern in the words, the SI was short.

Evaluation and a Method of Presentation of the Sound Output From the Lexiphone-A Reading Machine for the Blind

The operation of the Lexiphone, a reading machine for the blind, is described. The Lexiphone produces a sound pattern for each of the alphabet symbols, and the blind reader has to learn to associate each of these patterns with the corresponding letter. With practice, whole words and short phrases are recognized as entities. As the Lexiphone machine reads each line of print by scanning it with a column containing a large number of photodiodes (54), the visual resolution is quite high and the equivalent quantizing noise is low The signals from the photocells are processed by digital circuits to. produce the modulating signals of a single square wave. The square wave is modulated both in frequency and amplitude, the frequency component being the chief one to identify the letter, and the code sounds generated by the machine reported to be quite pleasant. The physical construction of the Lexiphone is robust and a description of the machine is given. The reading speed of the Lexiphone is discussed. Experiments indicate that a reading speed of over 30 words a minute including line change can be attained with 200 h of training (over a year). A method of dichotic presentation has been proposed to increase the reading speed and preliminary experiments have produced encouraging results.

Can Uncertainty Management be Realized in a Finite Totally Ordered Probability Algebra

Abstract In this paper, the feasibility of using finite totally ordered probability models under Aleliunass Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how these problems arise. The investigation shows that a finite probability model may be of very limited usage.