David Cyganski

Applications of Tensor Theory to Object Recognition and Orientation Determination

A method is developed by which images resulting from orthogonal projection of rigid planar-patch objects arbitrarily oriented in three-dimensional (3-D) space may be used to form systems of linear equations which are solved for the affine transform relating the images. The technique is applicable to complete images and to unlabeled feature sets derived from images, and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation, for use in object identification. No knowledge of point correspondence between images is required. Theoretical development of the method and experimental results are presented. The method is shown to be computationally efficient, requiring O(N) multiplications and additions where, depending on the computation algorithm, N may equal the number of object or edge picture elements.

Linear signal decomposition approach to affine-invariant contour identification

A means for the identification of objects from contours despite affine transform induced distortions that takes the form of a linear signal space decomposition has been obtained. This new technique also yields robust estimates of the affine transformation from which the 3-D rotations of a near planar object may be obtained. The ability to determine object identity and orientation from a singe model representation without iteration or combinatorial search proceeds from the use of affine invariant differential measures that may be derived via Lie group theory. The resulting technique is extremely robust in the presence of noise (or nonplanarity of the object) owing to the error rejection properties of the signal space projection operations. The resulting algorithm is amenable to high-speed implementation with digital signal processing hardware architectures because it can be reduced to a sequence of linear 1-D signal processing operations. Included in this paper are a number of demonstration results that illustrate the resilience of the solutions in the presence of severe nonaffine distortion and pixelization error.

A linear signal decomposition approach to affine invariant contour identification

Means for the identification of objects from contours despite affine transform induced distortions using a linear signal space decomposition are described. This technique also yields robust estimates of the 3-D rotations of a near planar object. The ability to determine object identity and orientation from a single model representation without iteration or combinatorial search proceeds from the use of affine invariant differential measures derived via Lie group theory. The technique is extremely robust owing to the error rejection properties of signal space projections. Results illustrating the resilience of the solutions in the presence of severe non-affine distortion and pixelization are given.

Determination of 3-D object orientation from projections

A method is presented for determination of the orientation in 3-space of 3-D objects without point correspondence information and without requiring only differential motion between images. Either 2-D projections or 3-D surface coordinate information may be used.

Generation of affine invariant local contour feature data

Abstract A method for determining 3-D object orientation from a single 2-D image with incomplete data is discussed. Locally determined affine invariant data from planar object features allows efficient solution for transformation parameters using the generalized Hough transform.

Object identification and orientation determination in 3-space with no point correspondence information

The problem of identification of rigid planar-patch objects from images projected from random orientations in 3-D space is approached using tensor representation of image measures. This allows standardization of object orientation without knowledge of object identity, and hence permits a simple one-step comparison operation between the standardized unknown and each library image. Geometric transformations due to oblique viewing angles, as well as translation, rotation, and scale change are handled. Experimental results using a library of camera-acquired images demonstrate correct performance of the algorithm.

Design of a System for Automated Measurement and Statistics Calculation of Voltage and Current Harmonics

The design and operation of a portable, personal computer-based system for the measurement and processing of data on 60 Hz. and harmonic current and voltage amplitudes and phases, and for the production of statistics and time trends on those quantities is described. Over the data acquisition interval, which may be several days in length, the system calculates and stores for each selected harmonic frequency of each selected voltage or current channel, statistics chosen from among: Mean, Mean Square Value, Variance, Maximum, Minimum. Trends in composite quantities such as Telephone Influence Factor and Total Harmonic Distortion may also be calculated over the interval. Samples of the graphical presentation of statistical results are included.

Analytic Hough transform

An analytic extension of the Hough Transform is introduced and analyzed, and an implementation is demonstrated. The Hough Transform in its usual implementation has proven to be a useful tool for image segmentation and feature extraction through identification of approximately coffinear point sets in images. The Analytic Hough Transform (AliT) algorithm significantly improves upon these results by operating specifically with the information in spatially quantized images to yield those pixel sets that exactly define digital lines in the image. The resulting pixel sets, while being subsets of a digital line set, need not be contiguous. Thus the AHT also represents an alternative to digital line tests that depend upon contiguity. An Inverse Analytic Hough Transform (IAHT) is also introduced. For a given quantized image the AliT segments its Hough parameter space into convex polygons that represent all real line sets that pass entirely through certain digital line pixel sets in the image. The IAHT converts these parameter space polygons into a pair of convex hulls in image space. A real line passes between these hulls if and only if it passes through every pixel connected with the parameter space polygon. Thus the IAHT generates a pair of simple geometric boundaries in image space that associate pixels with polygonal AliT solution regions. An implementation of the AliT is discussed and demonstrated. It is found that the AliT, with its exact results, can be a computationally attractive alternative to the usual implementation of a high resolution Hough Transform. Furthermore, the AliT and the IAHT effectively couple and efficiently find exact solutions to the problems of digital line detection and determination of associated real line parameters.

Comparison of bit and word level algorithms for evaluating unstructured functions over finite rings

We study the problem of implementing multivariate functions defined over finite rings or fields as parallel circuits. Such functions are essential for building cryptographic substitution boxes and hash functions. We present a modification to Horners algorithm for evaluating arbitrary n-variate functions defined over finite rings and fields. Our modification is based on eliminating redundancies in the multivariate version of Homers algorithm which occur when the evaluation takes place over a small finite mathematical structure and may be considered as a generalization of Shannons lower bound and Mullers algorithm to word level circuits. If the domain is a finite field GF(p) the complexity of multivariate Horner polynomial evaluation is improved from O(p n ) to O(p n 2n). We prove the optimality of the presented algorithm. Our comparison of the bit level approach to the optimized word level approach yields an interesting result. The bit level algorithm is more efficient in both area consumption and time delay. This suggests that unstructured functions over finite rings or fields should be implemented using the bit-level approach and not the commonly used word level implementation style.

Efficient implementation of the analytic Hough transform for exact linear feature extraction

In this paper an implementation of the analytic Hough transform (AHT) for exact digital line detection is developed that employs a new, efficient data structure. This new structure eliminates the need to represent each digital line parameter region that is developed during the analysis of the image by empolying a region divider representation. A relative storage scheme is employed thast permits reconstruction of region occupancy information during the search for digital line support. Furthermore, it is shown that all values in the AHT data structure may be stored as rational numbers with fixed and finite numerator and denominator ranges defined by the image resolution. As a result, all floating point computations are replaced by faster, fixed word-size, integer operations.