One of the classic results of mathematical morphology is the filter-representation theorem of G. Matheron (1975) for black-and-white images. The theorem states that any morphological filter can be represented as a uni...
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ISBN:
(纸本)081861952x
One of the classic results of mathematical morphology is the filter-representation theorem of G. Matheron (1975) for black-and-white images. The theorem states that any morphological filter can be represented as a union of erosions by elements in the filter's kernel. In its dual form, it states that the erosion representation can be replaced by an intersection of dilations by elements of the dual filter's kernel. Here, the dual-form of the gray-scale representation is derived in terms of a minimum of dilations by elements in the dual filter's kernel.
The authors present an iterative algorithm for the recovery of 2-D motion, i.e., an algorithm for the determination of a transformation which maps one image onto another. The local ambiguity in measuring the motion of...
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ISBN:
(纸本)081861952x
The authors present an iterative algorithm for the recovery of 2-D motion, i.e., an algorithm for the determination of a transformation which maps one image onto another. The local ambiguity in measuring the motion of contour segments (called the aperture problem) makes it necessary to rely on measurements along the normal direction. Since the measured normal flow itself does not agree with the actual normal flow, the full flow recovered from this erroneous normal flow possesses substantial error too, and any attempt to recover the 3-D motion from such full flow is doomed to failure. The present method is based on the observation that a polynomial approximation of image flow provides sufficient information for 3-D motion computation. The use of an explicit flow model makes it possible to improve normal flow estimates through an iterative process. The algorithm has been tested on synthetic and simple natural time-varying images. The image flow recovered from this scheme was sufficiently accurate as to be useful in 3-D structure and motion computation.
The authors examine two important problems, estimation of goodness of fit, in modeling binary single-texture images by discrete Markov random fields. A methodology for comparing parameter estimators is proposed and ap...
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ISBN:
(纸本)081861952x
The authors examine two important problems, estimation of goodness of fit, in modeling binary single-texture images by discrete Markov random fields. A methodology for comparing parameter estimators is proposed and applied to evaluate four estimation procedures. The classes of models considered are four-parameter Derin-Elliot models and four-parameter autobinomial models with second-order neighborhoods. A Min-χ2 estimator is proposed and shown to outperform estimators described in the literature. The methodology is based on a hardcore sampling process over the parameter space and a Wilcoxon rank-sum statistic. A static for assessing the goodness of fit between a specific model and an arbitrary texture image is also proposed and used in a Monte Carlo ranking test. The statistic is experimentally validated on synthetic textures. Experiments on natural textures suggest that second-order binary models do not fit natural textures well.
A novel algorithm for three-dimensional edge detection is proposed. This method is an extension to the 3-D case of the optimal 2-D edge detector recently introduced by R. Deriche (1987). The authors present better the...
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ISBN:
(纸本)081861952x
A novel algorithm for three-dimensional edge detection is proposed. This method is an extension to the 3-D case of the optimal 2-D edge detector recently introduced by R. Deriche (1987). The authors present better theoretical and experimental performances than some classical approaches used previously. Experimental results obtained on magnetic-resonance images and on echographic images are shown. It is pointed out that this approach can be used to detect edges in other multidimensional data, for instance, 2D + t or 3D + t images.
Edge detection is analyzed as a problem in cost minimization. A cost function is formulated that evaluates the quality of edge configurations. A mathematical description of edges is given, and the cost function is ana...
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ISBN:
(纸本)081861952x
Edge detection is analyzed as a problem in cost minimization. A cost function is formulated that evaluates the quality of edge configurations. A mathematical description of edges is given, and the cost function is analyzed in terms of the characteristics of the edges in minimum-cost configurations. The cost function is minimized by the simulated annealing method. A novel set of strategies for generating candidate states and a suitable temperature schedule are presented. Sequential and parallel versions of the annealing algorithm are implemented and compared. Experimental results are presented.
A method of learning structural models or 2-D shape from real data is described and demonstrated. These models can be used to classify nonrigid shapes, even if they are partially occluded, and to label their parts. Th...
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ISBN:
(纸本)081861952x
A method of learning structural models or 2-D shape from real data is described and demonstrated. These models can be used to classify nonrigid shapes, even if they are partially occluded, and to label their parts. The representation of a single shape is a layered graph whose vertices correspond to n-ary relations. A class of shapes is represented as a probability model whose outcome is a graph. The method is based on two types of learning: unsupervised learning used to discover relations, and supervised learning used to build class models. The class models are constructed incrementally, by matching and merging graphs representing shape instances. This process uses a fast graph-matching heuristic which seeks a simplest representation of a graph. An important feature is the self-generation of symbolic primitives by an unsupervised learning process. This feature makes it possible to apply the system to any set of shape data without adjustments, while other methods might require the user to provide a different set of primitives for each case.
A robust edge-detection algorithm which performs equally under a wide variety of noisy situations and a broad range of edges is described. The algorithm is executed in three phases. In phase 1, the step and linear edg...
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ISBN:
(纸本)081861952x
A robust edge-detection algorithm which performs equally under a wide variety of noisy situations and a broad range of edges is described. The algorithm is executed in three phases. In phase 1, the step and linear edges are detected from the noise-corrupted image using a statistical classification technique. In phase 2, all the thin-line edges (i.e., which are lines less than two pixels wide) are detected by a supplementary technique since these edges cannot be detected simultaneously with the other step and linear edges. In phase 3, the spurious edge elements are suppressed and the isolated missing edge elements are interpolated using a number of hypothesized edge-segments. Finally some experimental results are provided to illustrate the success of the algorithm.
A nonlinear least-squares optimization technique is proposed which uses the Levenberg-Marquardt method and estimates the motion and structure parameters to a global scale factor by minimizing an objective function. Th...
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ISBN:
(纸本)081861952x
A nonlinear least-squares optimization technique is proposed which uses the Levenberg-Marquardt method and estimates the motion and structure parameters to a global scale factor by minimizing an objective function. This objective function is the mean-square difference between the measured coordinates of feature points in the image plane and the coordinates predicted from the current state estimate. In comparison to existing approaches, this technique converges faster and yields better estimates. A recursive version of this algorithm is developed using the block approach. This algorithm is shown to also track eventful motion effectively. The performance of the proposed technique on real image sequences is also presented. Some performance results are indicated to illustrate the efficacy of this approach.
A novel technique for computing intrinsic surface properties is developed. Intrinsic surface properties refer to those properties of a surface which are not affected by the choice of the coordinate system, the positio...
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ISBN:
(纸本)081861952x
A novel technique for computing intrinsic surface properties is developed. Intrinsic surface properties refer to those properties of a surface which are not affected by the choice of the coordinate system, the position of the viewer relative to the surface, and the particular parametric representation used to describe the imaged surface. Since intrinsic properties are characteristics of a surface, they are ideal for the purpose of representation and recognition. The intrinsic properties of interest here are the principal curvatures, the intrinsic distance, and the lines of curvature. The authors adopt a structured lighting sensing configuration where a grid pattern is projected to encode the object surfaces for analysis. At each stripe junction, the curvature of the projected stripe on the object surface is computed and related to that of the normal section which shares the same tangential direction as the projected curve. The principal curvatures and the their directions at the stripe junction under consideration are then recovered using Euler's theorem.
Conventional approaches to dynamic scene analysis do not use motion itself explicitly for recognition. The authors propose a different approach for the use of motion in a computer vision system which uses the motion c...
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ISBN:
(纸本)081861952x
Conventional approaches to dynamic scene analysis do not use motion itself explicitly for recognition. The authors propose a different approach for the use of motion in a computer vision system which uses the motion characteristics of moving objects without actually recovering the structure. In this approach, the extended trajectories followed by the objects are considered. It is argued that in many cases, where an object has a fixed and predefined motion, the trajectory of several points may serve to uniquely identify the object. In this approach, the trajectories are analyzed at multiple scales to identify important events corresponding to discontinuities in direction, speed, and acceleration using scale space. These important events are recorded in a presentation called trajectory primal sketch. Experimental results are presented graphically, demonstrating the potential value of this approach.
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