Xinhua Zhuang

Image Analysis Using Mathematical Morphology

For the purposes of object or defect identification required in industrial vision applications, the operations of mathematical morphology are more useful than the convolution operations employed in signal processing because the morphological operators relate directly to shape. The tutorial provided in this paper reviews both binary morphology and gray scale morphology, covering the operations of dilation, erosion, opening, and closing and their relations. Examples are given for each morphological concept and explanations are given for many of their interrelationships.

Pose estimation from corresponding point data

Solutions for four different pose estimation problems are presented. Closed-form least-squares solutions are given to the overconstrained 2D-2D and 3D-3D pose estimation problems. A globally convergent iterative technique is given for the 2D-perspective-projection-3D pose estimation problem. A simplified linear solution and a robust solution to the 2D-perspective-projection-2D-perspective-projection pose-estimation problem are also given. Simulation experiments consisting of millions of trials with varying numbers of pairs of corresponding points and varying signal-to-noise ratios (SNRs) with either Gaussian or uniform noise provide data suggesting that accurate inference of rotation and translation with noisy data may require corresponding point data sets with hundreds of corresponding point pairs when the SNR is less than 40 dB. The experimental results also show that the robust technique can suppress the blunder data which come from outliers or mismatched points. >

Morphological structuring element decomposition

Abstract To efficiently perform morphological operations with specialized pipeline hardware which is not able to utilize all the points in the domain of the structuring element in one pipeline stage requires the capability of decomposing the structuring element into a morphological dilation of smaller structuring elements each of which is utilized in a successive stage of the pipeline. In this paper, we give the theory and algorithm for such optimal structuring element decomposition.

The digital morphological sampling theorem

Morphological sampling reduces processing time and cost and yet produces results sufficiently close to the result of full processing. A morphological sampling theorem is described which states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriate morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology, and then it is extended to gray-scale morphology through the use of the umbra homomorphism theorems. >

Pipeline architectures for morphologic image analysis

The concepts of mathematical morphology provide some very powerful tools with which low-level image analysis can be performed. Low-level analysis, by its very nature, involves repeated computations over large, regular data structures. Parallelism appears to be a necessary attribute of a hardware system which can efficiently perform such image-analysis tasks, and there is a variety of forms that this parallelism can take. This paper gives a tutorial description of the basic morphological transformations and demonstrates how the basic morphological transformations can be implemented in the pipeline processing form of parallelism. Correspondingly, plausible designs for pipeline architectures are developed.

A simplex-like algorithm for the relaxation labeling process

A simplex-like algorithm is developed for the relaxation labeling process. The algorithm is simple and has a fast convergence property which is summarized as a one-more-step theorem. The algorithm is based on fully exploiting the linearity of the variational inequality and the linear convexity of the consistent-labeling search space in a manner similar to the operation of the simplex algorithm in linear programming. >

Binary morphology: working in the sampled domain

A description is given of the relationship between morphologically filtering and then sampling vs. sampling, and then morphologically filtering in the sampled domain. The authors also describe the relationship between morphologically filtering vs. sampling, morphologically filtering in the sampled domain, and then reconstructing. Unlike the standard communication sampling theory where for appropriately low-pass filtered images there is commutivity between sampling and filtering, this is not the case for appropriately morphologically simplified images. The relationship which does exist shows that the commutivity holds to within one sampling interval distance in the unsampled domain and to within two sampling intervals in the sampled domain.<<ETX>>

Recovering 3-D motion parameters from image sequences with gross errors

A robust algorithm to estimate 3-D motion parameters from a sequence of extremely noisy images is developed. The noise model includes correspondence mismatch errors, outliers, uniform noise, and Gaussian noise. More than 100000 controlled experiments were performed. The experimental results show that the error in the estimated 3-D parameters of the linear algorithm almost increases linearly with fraction of outliers. However, the increase for the robust algorithm is much slower, indicating its better performance and stability with data having blunders. The robust algorithm can detect the outliers, mismatching errors and blunders up to 30% of observed data. Therefore, it can be an effective tool in estimating 3-D motion parameters from multiframe time sequence imagery.<<ETX>>

From depth and optical flow to rigid body motion

The authors develop an algorithm to determine uniquely the rigid body motion from optical flow and depth, where the depth, however, does not involve any derivative information. Thus, the original assumptions made by D.H. Ballard and O.A. Kimball (1983) and by R.M. Haralick and X. Zhuang (1986) are relaxed. The proposed algorithm is appealing; in contrast to the existing linear optical flow-motion algorithms, it requires only three instead of eight optical flow image points.<<ETX>>

A note on “rigid body motion from depth and optical flow”

A theoretical solution to the problem “Rigid Body Motion from Depth and Optical Flow” is uniquely determined, given four uncoplanar initial spatial points and, associated with them, optical flow and depth information. A numerical example is given to explain the theory and related algorithm.