## Vol. 4 (1995): Abstracts of Papers

## Machine GRAPHICS & VISION, Vol. 4 (1995), Nos. 1/2:

Tuzikov A.V., Zalesskii P.A.: **Morphological operations on complete lattices and their symmetries**.

MGV vol. 4, nos. 1/2, 1995, pp. 3-28.

We consider mathematical morphology transformations on complete lattices. The problem of symmetry preservation under morphological transformations is investigated. We introduce also an approach of generating so called *G*-transformations which are invariant to a group of lattice automorphisms *G*. These transformations preserve symmetries of the original image (lattice element) belonging to the group *G*. Such transformations as skeleton, hit-or-miss, thickening, thinning are also considered. **Key words**: mathematical morphology, complete lattice, invariant transformation, symmetry.

Chmielewski L.: **A note on merging line segments with the search space reduced by a condition based on an ordering**.

MGV vol. 4, nos. 1/2, 1995, pp. 29-38.

The problem of merging line segments into more meaningful, longer segments involves deciding which segments to merge. The full solution space would be searched if each segment were checked with each other one for possible match. The entire process should be repeated if segments merged in a previous step were many. For some types of segments, such an ordering relation can be found that only for the segments which are close to each other in this order the merging is probable. The condition of closeness in the order can be used to significantly reduce the search space. This simple observation is independent of the segment type and of the form of a sufficient condition for merging. Examples of merging linear segments are presented. **Key words**: merging, search space reduction, line segments.

Boult T., Melter R. A., Skorina F., Stojmenovic I.: **Applications of G-neighbors to image processing and morphology**.

MGV vol. 4, nos. 1/2, 1995, pp. 39-58.

Image processing often involves operations using pixel "neighborhoods". This paper combines the usual definition of 4 or 8 connected neighbors with image information to produce local neighbor definitions that are signal dependent. These generalized neighbors, G-neighbors, can be used in a variety of image processing tasks. The paper examines their use in detail preserving smoothing and morphology. The simple/local nature of G-neighbor definitions make them ideal for implementation on low-level pixel parallel hardware. A near real-time parallel implementation of the G-neighbor computation, including G-neighbor-based detail preserving smoothing and G-neighbor morphology, is discussed. The paper includes a qualitative comparison of G-neighbor-based algorithms to previous work.

Palenichka R., Klette R., Koschan A., Kuchynsky T.: **A fast algorithm for edge structure detection in monochrome and color images**.

MGV vol. 4, nos. 1/2, 1995, pp. 59-77.

A new hierarchical algorithm for robust edge structure detection in monochrome and color images is proposed. This edge detector is based on the estimation procedure for edge (or no-edge) probability, thus allowing an explicit accuracy control during the edge detection. The necessary calculations are organized in computation saving manner by using the principle of spatial recursion. **Key words**: image modeling, mathematical morphology, edge detection, image filtering, feature extraction, spatial recursion.

Kopp M., Purgathofer W.: **Efficient 3*3 median filter computations**.

MGV vol. 4, nos. 1/2, 1995, pp. 79-82.

This paper presents an efficient algorithm for median filtering with a 3*3 filter kernel with only about 9 comparisons per pixel using spatial coherence between neighbouring filter computations. The basic algorithm calculates two medians in one step and reuses sorted slices of three vertical neighbouring pixels. An extension of this algorithm for 2D spatial coherence is also examined, which calculates four medians per step. Even though theoretical results would yield 5% performance increase compared to the basic algorithm, experimental results showed less significant increase or even worse performance dependent on the hardware. **Key words**: image processing, filtering, 3*3 median kernel, spatial coherence.

Klopotek M.A.: **Distribution of degrees of freedom over structure and motion of rigid bodies**.

MGV vol. 4, nos. 1/2, 1995, pp. 83-100.

This paper is concerned with recovery of motion and structure parameters from multiframes under orthogonal projection when only points are traced. The main question is how many points and/or how many frames are necessary for the task. It is demonstrated that 3 frames and 3 points are the absolute minimum. Closed-form solution is presented. Furthermore, it is shown that the task may be linearized if either four points or four frames are available. It is demonstrated that no increase in the number of points may lead to recovery of structure and motion parameters from two frames only. It is shown that instead the increase in the number of points may support the task of tracing the points from frame to frame.

Ignatiev V.M., Abusova I.V.: **Quality evaluation of pictures in composite displays**.

MGV vol. 4, nos. 1/2, 1995, pp. 101-108.

In the article the authors have discussed problems of video-data loss evaluation in display with screens being composed of separate fragments, each of which is synthesized with an individual cathode-ray tube. There is a classification of the factors distorting primary given forms and causing the data loss in an interfragment space. The main mathematical relations, making it possible to calculate these losses, have been deduced. Based on theoretical investigations test tables for evaluation of quality of compatibility of separate fragments into an integral picture have been proposed. **Key words**: display, large-size screen, resolution.

Hall T.: **Issues in the use of computer visualisation by planning agencies**.

MGV vol. 4, nos. 1/2, 1995, pp. 109-122.

Computer visualisation has a still largely unrealised potential for enabling planning agencies and the public to evaluate the visual impact of proposed development. Its advantages arise not only from its ability to produce realistic images but also from its ability to assist negotiations between the parties through the interactive manipulation of these images. The author has tested this assertion by visualising a number of real life examples dealt with by selected British planning authorities and assessing the impact on the decision making process. The results point to the conclusion that the utility of visualisation turns on its acceptance by all parties to the negotiations. When this achieved, issues such as the level of realism to be employed and the degree of objectivity to be accorded to the images can also be resolved in relation to the cost of achieving them.

Michelitsch T., Michelitsch M.: **A Mandelbrot set of the transcendental mapping c*cos z with special initial conditions**.

MGV vol. 4, nos. 1/2, 1995, pp. 125-130.

A Mandelbrot set of a transcendental map with other than the "usual" initial condition, i. e. *z0* = 0, exhibits in the vicinity of its boundary surprizing structures. Many of them seem to have similar structures as the corresponding Julia sets generated by c-parameters from corresponding inner areas from both the "standard" Mandelbrot set and the "transcendental" one. **Key words**: Mandelbrot set, Julia set, transcendental mappings, complex variables, initial conditions, computer experiments, fractals.

## Machine GRAPHICS & VISION, Vol. 4 (1995), Nos. 3/4:

Mursajew A.H., Olech B., Soldek J.: **Implementation of a new coding scheme for ray tracing subdivision algorithms**.

MGV vol. 4, nos. 3/4, 1995, pp. 137-149.

An effective approach to accelerate calculations while ray-tracing is to decrease the voxels' size. But this causes an increase in the voxels amount and requires a huge memory to store the specification of a concrete scene. To overcome this contradiction it is necessary to organize a fast access to the objects included in a voxel and to limit the amount of voxels that are to be stored and analyzed. A compact scene representation in the form of bit arrays with hierarchical organization of data access has been introduced as a tool for the new coding scheme to solve the problem in question. Each bit of these tables is associated with the property (emptiness/nonemptiness) of certain subspace. This particular feature was the base for a hardware module, convenient but not indispensable, that enables the data-access time to be decreased to a negligible value at considerable memory requirements. **Key words**: computer graphics, space subdivision, hierarchy traversal, hardware ray-tracing.

Kolingerova I.: **Detection of mutual position of a point and a convex polygon in E^2**.

MGV vol. 4, nos. 3/4, 1995, pp. 151-160.

The paper deals with algorithms for point-in-convex-polygon problem solution. It tries to find some compromise between effective, but difficult to implement methods and easy, but slow ones. Both well-known and new accelerating techniques are presented and results of their testing and comparison are given. **Key words**: convex polygon, point, accelerating techniques, computer graphics.

Bartkowiak A., Szustalewicz A.: **The augmented biplot and some examples of its use**.

MGV vol. 4, nos. 3/4, 1995, pp. 161-185.

Biplot is an explorative method of data analysis permitting to represent graphically, usually in a plane, the interrelations among points-variables and points-individuals located in a multivariate space. This is done by making projections from the multivariate space onto two- or three-dimensional subspaces. The crucial issue is: to what extend the projections in the lower dimension subspaces reflect the true relations of points-variables and points-individuals in the full data space? It happens that sometimes the representation given by the biplot is a good one, however sometimes it is a bad one and certainly not sufficient.

We show exactly wherefrom (i.e. from which theorems) some inferential properties of a biplot can be deduced and under which circumstances the relations visualized in the biplot are trustworthy.

We propose to construct the biplot in an extended mode which permits to judge the adequacy of the two-dimensional approximation visualized by the classical biplot. We call the biplot drawn in the extended mode the it augmented biplot.

Several real data examples illustrate the use of the augmented biplot and the broadness and diversity of problems which can be elucidated relatively simply by use of the elaborated technique. **Key words**: data matrix, exploratory data analysis, reduction of dimensionality, graphical representation of multivariate points and interrelations from multivariate space.

Klopotek M.A.: **Rigid body structure and motion from two-frame point-correspondences under perspective projection**.

MGV vol. 4, nos. 3/4, 1995, pp. 187-202.

This paper is concerned with possibility of recovery of motion and structure parameters from multiframes under perspective projection when only points on a rigid body are traced. Free (unrestricted and uncontrolled) pattern of motion between frames is assumed. The major question is how many points and/or how many frames are necessary for the task. It has been shown in an earlier paper, that for orthogonal projection two frames are insufficient for the task. The paper demonstrates that under perspective projection total uncertainty about relative position of focal point versus projection plane makes the recovery of structure and motion from two frames impossible.

Kulikowski J.L.: **Fast algorithms of linear discrete image filtering**.

MGV vol. 4, nos. 3/4, 1995, pp. 203-211.

The paper describes a concept of linear image filtering algorithm minimizing the number of needed time-consuming arithmetic operations. Due to the symmetry of linear convolution kernels as well as to the fact that certain pixel-values are used several times within the filtering process, the number of operations can be reduced from 3 to 7 times by preliminary calculation and storage of needed transitional results. The method can be extended on 3D images filtering. **Key words**: computer-aided image processing, discrete linear filters, computing complexity.

Revievers' index

Authors' index

Contents of volume 4, 1995