Zenon Kulpa

Area and perimeter measurement of blobs in discrete binary pictures

In picture processing one is often confronted with the problem of deriving some geometrical parameters (e.g., area, perimeter) of continuous figures (blobs, curves) from their digitizations. This paper concerns some particular aspects of this problem, namely, the construction of practical, simple, and computationally fast methods for measuring accurately the area and perimeter of blobs given as digital binary pictures. The analysis of some properties of digital pictures leads to two such methods. The first one uses only local, position-invariant parallel picture processing operations. The second one uses explicit polygonal approximations of the picture contour, with controlled degree of approximation, and can work on more noisy pictures. The methods were practically tested in a working program for shape factor measurement of fiber sections. In addition some useful properties of Freemans digitization scheme are investigated and proved.

On the properties of discrete circles, rings, and disks

This paper is about formal properties of discrete circles (defined as Freeman digitizations of circles with integer radius and center coordinates), discrete disks (defined as discrete circles with filled-in interiors), and discrete rings (defined as differences between consecutive discrete disks). Such objects are important in applications involving distance transforms and propagation methods. Several properties of these objects are derived, namely, conditions for occurrence of certain point configurations, formulas for the number of raster points in these objects, and their perimeters and areas. These parameters are also related to corresponding properties of ideal (nondiscrete) circles, and some limit theorems (for radius approaching infinity) are stated.

Putting order in the impossible

The class of visual illusions called ‘impossible figures’ (illusory spatial interpretations of pictures) is analyzed in order to introduce an ordering into the great variety of such figures. Such an ordering facilitates reference, unifies terminology, and establishes a conceptual framework for further investigations of the subject, making easier the choice and systematic generation of various types of figures (for example, in systematic psychological experiments). First, the notion of ‘impossible figure’ is defined and certain other related classes of figures (so-called ‘likely’ and ‘unlikely’ figures) are distinguished. Second, the fundamental ‘impossibility sources’ are identified as elementary ‘building blocks’ of all impossible figures. Finally, two broad classes of impossible figures, multibars (or ‘impossible polygons’) and striped figures, are briefly described.

Are impossible figures possible

Abstract In the paper, a thorough analysis of the so-called impossible figures phenomenon is attempted. The notion of an impossible figure and some other related phenomena (e.g. ‘likely’ and ‘unlikely’ figures) are precisely defined and analyzed. It is shown that all these figures, being illusions of spatial interpretation of pictures, are more relevant to psychology of vision (and related artificial intelligence research) than to geometry or mathematics in general. It suggests an inadequacy of several previous formal approaches to explain these phenomena and to deal with them in computer vision programs. The analysis of these spatial interpretation illusions allows us to formulate several properties of the structure of our spatial interpretation mechanism. A two-stage structure of this mechanism, a set of basic ‘interpretation assumptions’ and a set of basic ‘impossibility causes’ are identified as a result.

Diagrammatic representation for interval arithmetic

Abstract The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithmetic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties.

Diagrammatic Representation of Interval Space in Proving Theorems about Interval Relations

The paper presents two-dimensional graphical representations for the space of intervals (the IS-diagram) and arrangement interval relations (the W-diagram). The usefulness of the representations is illustrated with the example of proving equivalence of different characterizations of convex interval relations.

More about areas and perimeters of quantized objects

Abstract A controversy between two common approaches to area and perimeter measurement of discrete blobs is resolved in this paper. The first approach takes the chain of 8-connected border pixels as the object boundary (thus using Picks theorem to exclude a contribution of a part of these to the value of the area), whereas the second one considers the boundary of the object to be a line separating object-border pixels from background ones (thus counting all pixels of the object as its area). It is shown that the validity of these approaches (and corresponding measurement methods) is related to the digitization scheme assumed: the first approach is valid for a boundary-line digitization (or edge-detection) scheme, and the second one is better for a point-sampling digitization (or region-extraction or thresholding) scheme.

A diagrammatic approach to investigate interval relations

Abstract This paper describes several diagrammatic tools developed by the author for representing the space of intervals and especially interval relations. The basic tool is a two-dimensional, diagrammatic representation of space of intervals, called an MR-diagram . A diagrammatic notation based on it, called a W-diagram , is the main tool for representing arrangement (or Allen ’ s ) interval relations . Other auxiliary diagrams, like conjunction and lattice diagrams, are also introduced. All these diagrammatic tools are evaluated by their application to various representational and reasoning tasks of interval relations research, producing also certain new results in the field.

Digital Image Processing Systems

Universal digital image processing systems in europe - A comparative survey.- Cello an interactive system for image analysis.- A knowledge-based interactive robot-vision system.- Real-time processing of binary images for industrial applications.- CPO-2/K-202: A universal digital image analysis system.- The gop parallel image processor.- Object detection in infrared images.

Algorithms for circular propagation in discrete images

Abstract Several algorithms implementing circular propagation on discrete pictures are described. After a general description of discrete circular objects (serving as basic primitives in circular propagation) and a general introduction to the area of propagation methods, several exact and approximate algorithms of circular propagation are described in detail. The algorithms are devised so as to be especially effective in picture processing environments based on parallel or semiparallel local operations on pictures.