Fitting a two-joint orthogonal chain to a point set

We study the problem of fitting a two-joint orthogonal polygonal chain to a set S of n points in the plane, where the objective function is to minimize the maximum orthogonal distance from S to the chain. We show that this problem can be solved in Θ(n) time if the orientation of the chain is fixed, and in Θ(n log n) time when the orientation is not a priori known. We also consider some variations of the problem in three-dimensions where a polygonal chain is interpreted as a configuration of orthogonal planes. In this case we obtain O(n) and O(n log n) time algorithms depending on which plane orientations are fixed.Postprint (published version

Proceedings of the NASA Workshop on Image Analysis

Three major topics of image analysis are addressed: segmentation, shape and texture analysis, and structural analysis

Medial Axis Transform using Ridge Following

The intent of this investigation has been to find a robust algorithm for generation of the medial axis transform (MAT). The MAT is an invertible, object centered, shape representation defined as the collection of the centers of disks contained in the shape but not in any other such disk. Its uses include feature extraction, shape smoothing, and data compression. MAT generating algorithms include brushfire, Voronoi diagrams, and ridge following. An improved implementation of the ridge following algorithm is given. Orders of the MAT generating algorithms are compared. The effects of the number of edges in the polygonal approximation, shape area, number of holes, and number/distribution of concave vertices are shown from test results. Finally, a set of useful extensions to the ridge following algorithm are discussed

Part Description and Segmentation Using Contour, Surface and Volumetric Primitives

The problem of part definition, description, and decomposition is central to the shape recognition systems. The Ultimate goal of segmenting range images into meaningful parts and objects has proved to be very difficult to realize, mainly due to the isolation of the segmentation problem from the issue of representation. We propose a paradigm for part description and segmentation by integration of contour, surface, and volumetric primitives. Unlike previous approaches, we have used geometric properties derived from both boundary-based (surface contours and occluding contours), and primitive-based (quadric patches and superquadric models) representations to define and recover part-whole relationships, without a priori knowledge about the objects or object domain. The object shape is described at three levels of complexity, each contributing to the overall shape. Our approach can be summarized as answering the following question : Given that we have all three different modules for extracting volume, surface and boundary properties, how should they be invoked, evaluated and integrated? Volume and boundary fitting, and surface description are performed in parallel to incorporate the best of the coarse to fine and fine to coarse segmentation strategy. The process involves feedback between the segmentor (the Control Module) and individual shape description modules. The control module evaluates the intermediate descriptions and formulates hypotheses about parts. Hypotheses are further tested by the segmentor and the descriptors. The descriptions thus obtained are independent of position, orientation, scale, domain and domain properties, and are based purely on geometric considerations. They are extremely useful for the high level domain dependent symbolic reasoning processes, which need not deal with tremendous amount of data, but only with a rich description of data in terms of primitives recovered at various levels of complexity

Image analysis using visual saliency with applications in hazmat sign detection and recognition

Visual saliency is the perceptual process that makes attractive objects stand out from their surroundings in the low-level human visual system. Visual saliency has been modeled as a preprocessing step of the human visual system for selecting the important visual information from a scene. We investigate bottom-up visual saliency using spectral analysis approaches. We present separate and composite model families that generalize existing frequency domain visual saliency models. We propose several frequency domain visual saliency models to generate saliency maps using new spectrum processing methods and an entropy-based saliency map selection approach. A group of saliency map candidates are then obtained by inverse transform. A final saliency map is selected among the candidates by minimizing the entropy of the saliency map candidates. The proposed models based on the separate and composite model families are also extended to various color spaces. We develop an evaluation tool for benchmarking visual saliency models. Experimental results show that the proposed models are more accurate and efficient than most state-of-the-art visual saliency models in predicting eye fixation.^ We use the above visual saliency models to detect the location of hazardous material (hazmat) signs in complex scenes. We develop a hazmat sign location detection and content recognition system using visual saliency. Saliency maps are employed to extract salient regions that are likely to contain hazmat sign candidates and then use a Fourier descriptor based contour matching method to locate the border of hazmat signs in these regions. This visual saliency based approach is able to increase the accuracy of sign location detection, reduce the number of false positive objects, and speed up the overall image analysis process. We also propose a color recognition method to interpret the color inside the detected hazmat sign. Experimental results show that our proposed hazmat sign location detection method is capable of detecting and recognizing projective distorted, blurred, and shaded hazmat signs at various distances.^ In other work we investigate error concealment for scalable video coding (SVC). When video compressed with SVC is transmitted over loss-prone networks, the decompressed video can suffer severe visual degradation across multiple frames. In order to enhance the visual quality, we propose an inter-layer error concealment method using motion vector averaging and slice interleaving to deal with burst packet losses and error propagation. Experimental results show that the proposed error concealment methods outperform two existing methods

A strategy for the visual recognition of objects in an industrial environment.

This thesis is concerned with the problem of recognizing industrial objects rapidly and flexibly. The system design is based on a general strategy that consists of a generalized local feature detector, an extended learning algorithm and the use of unique structure of the objects. Thus, the system is not designed to be limited to the industrial environment. The generalized local feature detector uses the gradient image of the scene to provide a feature description that is insensitive to a range of imaging conditions such as object position, and overall light intensity. The feature detector is based on a representative point algorithm which is able to reduce the data content of the image without restricting the allowed object geometry. Thus, a major advantage of the local feature detector is its ability to describe and represent complex object structure. The reliance on local features also allows the system to recognize partially visible objects. The task of the learning algorithm is to observe the feature description generated by the feature detector in order to select features that are reliable over the range of imaging conditions of interest. Once a set of reliable features is found for each object, the system finds unique relational structure which is later used to recognize the objects. Unique structure is a set of descriptions of unique subparts of the objects of interest. The present implementation is limited to the use of unique local structure. The recognition routine uses these unique descriptions to recognize objects in new images. An important feature of this strategy is the transference of a large amount of processing required for graph matching from the recognition stage to the learning stage, which allows the recognition routine to execute rapidly. The test results show that the system is able to function with a significant level of insensitivity to operating conditions; The system shows insensitivity to its 3 main assumptions -constant scale, constant lighting, and 2D images- displaying a degree of graceful degradation when the operating conditions degrade. For example, for one set of test objects, the recognition threshold was reached when the absolute light level was reduced by 70%-80%, or the object scale was reduced by 30%-40%, or the object was tilted away from the learned 2D plane by 300-400. This demonstrates a very important feature of the learning strategy: It shows that the generalizations made by the system are not only valid within the domain of the sampled set of images, but extend outside this domain. The test results also show that the recognition routine is able to execute rapidly, requiring 10ms-500ms (on a PDP11/24 minicomputer) in the special case when ideal operating conditions are guaranteed. (Note: This does not include pre-processing time). This thesis describes the strategy, the architecture and the implementation of the vision system in detail, and gives detailed test results. A proposal for extending the system to scale independent 3D object recognition is also given

Application of fuzzy theory to pattern recognition

Piecewise curve approximation is used to describe boundaries of objects in pictures and waveforms. The method consists of linear and quadratic piecewise polynomial approximations in which the error must not exceed a predetermined cost threshold. A fuzzy Bayes model is used to determine if a breakpoint exists within an interval In or between intervals In and In+1 and to determine whether these intervals can be merged for data compaction reasons. In order to achieve these objectives a new fast algorithm has been proposed which gives good curve/object fitting. This algorithm uses a technique for generating generalized inverse matrices once an initial generalized inverse matrix has been determined. The continuity requirements at the breakpoints are relaxed such that the only requirement is that the data point for interval In-1 is the starting point for interval In. Results of computer experiments with graphic outlines and radar data are reported

An investigation into the use of genetic algorithms for shape recognition

The use of the genetic algorithm for shape recognition has been investigated in relation to features along a shape boundary contour. Various methods for encoding chromosomes were investigated, the most successful of which led to the development of a new technique to input normalised 'perceptually important point' features from the contour into a genetic algorithm. Chromosomes evolve with genes defining various ways of 'observing' different parts of the contour. The normalisation process provides the capability for multi-scale spatial frequency filtering and fine/coarse resolution of the contour features. A standard genetic algorithm was chosen for this investigation because its performance can be analysed by applying schema analysis to the genes. A new method for measurement of gene diversity has been developed. It is shown that this diversity measure can be used to direct the genetic algorithm parameters to evolve a number of 'good' chromosomes. In this way a variety of sections along the contour can be observed. A new and effective recognition technique has been developed which makes use of these 'good' chromosomes and the same fitness calculation as used in the genetic algorithm. Correct recognition can be achieved by selecting chromosomes and adjusting two thresholds, the values of which are found not to be critical. Difficulties associated with the calculation of a shape's fitness were analysed and the structure of the genes in the chromosome investigated using schema and epistatic analysis. It was shown that the behaviour of the genetic algorithm is compatible with the schema theorem of J. H. Holland. Reasons are given to explain the minimum value for the mutation probability that is required for the evolution of a number of' good' chromosomes. Suggestions for future research are made and, in particular, it is recommended that the convergence properties of the standard genetic algorithm be investigated