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49.
ABSTRACTION AND SCALE-SPACE EVENTS IN IMAGE UNDERSTANDING
Helmut Mayer
Chair for Photogrammetry and Remote Sensing
Technical University Munich
Arcisstr. 21, 80290 Munich, Germany
Phone: +49-89-2105-2688, Fax: +49-89-2809573
E-mail: helmut@photo.verm.tu-muenchen.de
Commission III, Working Group 3
KEY WORDS: Vision, Modeling, Artificial_Intelligence, Abstraction, Scale-Space
ABSTRACT
Image understanding can be described as the process of making information implicit in an image explicit in terms of objects. This
implies a mapping of structured semantic information (symbols) to discrete noisy two-dimensional information (digital image). One
way of solving this ill-posed problem is to fuse results in different images which have been produced from a single image by smoothing
it with various degree. The smoothing reduces noise, but also changes the scale of the image, i.e. features are suppressed.
From a theoretical point of view the following questions arise: How can the abstraction of the description of objects be linked to the
suppression of features in images of smaller scale? How can this be used for the recognition of objects?
As an answer to these questions, the link between abstraction and events in the so-called "scale-space" which mainly result in the
elimination of substructures, is presented in this paper. Examples are sketched showing that this link has practical implications for the
extraction of objects from images as well as for generalization of objects in geographic information systems (GIS) or cartography.
1 INTRODUCTION
Image understanding is a research area where, in spite of all big
progress in theory and applications, its inherent complexity only
slowly becomes clear. People think about the world in abstract
concepts which describe a complex physical world. Concepts, like
road, building, etc., are very hard to define in a formal way which
can be implemented as a computer program. The central issue
for a formal definition is knowledge representation (Sowa 1995).
Another aspect is the knowledge which has to be represented. It
has to come from an application (e.g. Photogrammetry, Remote
Sensing, or GIS). Issues which have been addressed only recently
are the importance of context (Strat 1995) or the combination
of different kinds of information (information fusion (Clément
et al. 1993, McKeown 1991)). A special case is the fusion of
different scales (resolutions). That this can aid the interpretation
has been shown in (Steger et al. 1995). Scale in the context of
image sequences was treated in (Sester 1990). The goal of this
paper is to give some theoretical considerations which support
the use of multiple scales. Especially it will be shown how the
semantics of objects is linked to scale, i.e. how scale can help to
define concepts.
In psychology vision is thought of as a process that involves alot
of very specialized modules which interact in different directions
(i.e. bottom-up and top-down). There was and is a quarrel between
different researchers on the role of images, but newer results
suggest that there really is a kind of image processing used in
the path of reasoning. Kosslyn (1994) speculates that hypotheses
generated on the line of reasoning about objects are verified by
means of matching an image of the hypothesized objects created
by computer-graphics like techniques into the real image.
Kosslyns findings furthermore suggest that distinctions are
made between the description of singular objects and their spatial
relations as well as between class and instance processing. Singu-
lar objects can further be used together with their spatial relations
as substructure, i.e. parts, of more complex objects. Besides the
fact that this constitutes a hierarchy of objects based on the part-of
relation, there also is an abstraction linked to this. A settlement
has for instance a substructure made of buildings, roads etc. But
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
in addition to this it also has a new, more abstract, quality, as its
own size or characteristics (shopping, recreation etc. ).
Opposed to abstraction which deals with symbols, scale-space
theory (Lindeberg 1994) is concerned with sub-symbolic signal
(here: image) information. The scale-space is constructed by
smoothing the original image with Gaussian kernels of succes-
sively increasing width. A property of scale-space theory is that
additionally to the continuously evolving smoothing of the image
events occur. These events are annihilation, merge, split and cre-
ation of extrema. Because most structure in an image, like points,
edges, or lines are related to extrema. this means that also the
structure is changed significantly.
An interesting question is, how these events are related to the
abstraction of symbols describing objects in the image. Because
most of the events will result in one way or another in the anni-
hilation of extrema, structure will be lost, i.e. the information in
the image is simplified. A light smoothing will mainly decrease
noise. But greater amounts of smoothing will also destroy struc-
ture of objects (simplification). Substructure cannot be detected
any more and the emphasis of the image is laid on the compound
object. In certain ways this means that abstraction has occurred
by simple smoothing.
The paper is organized as follows: In section 2 a short review
on the term abstraction as well as a description of scale-space
events is given. The link between abstraction and scale-space
events is analyzed conceptually and empirically in section 3 In
section 4 conclusions are given.
2 ABSTRACTION AND SCALE-SPACE EVENTS
2.1 Abstraction and Models
Looking at the term abstraction one finds that there are a lot of
definitions forit. It can be defined as the “mental process of isolat-
ing a common element or explicating a relationship possessed by
a number of things" (Encyclopedia Britannica 1985). Accord-
ing to Brachman (1983) abstraction is a relation of type "is-a"
wherein a generic type is abstracted into an individual (e.g. “the
eagle” in “the eagle is an endangered species”). In (Encyclopedia
523
