SPECIAL BISC Seminar, 22 January 1997, 320 Soda, 4-5:00pm

Michael Lee (leem@cs.berkeley.edu)
Thu, 23 Jan 1997 13:35:58 +0100

Spatial relationships between fuzzy image objects


Isabelle Bloch

Ecole Nationale Superieure des Telecommunications
Departement Images - CNRS URA 820
46 rue Barrault - 75013 Paris - France

22 January 1997
320 Soda Hall


Model-based or case-based pattern recognition often relies on similarity
measures, designed for comparing shapes and objects according to several
aspects or features. Spatial information constitutes an important part of
these features in image processing and scene interpretation, and it is
either related to each object itself, or related to relationships between
objects. We address in this presentation the problem of describing such
relationhips dedicated to model-based object recognition in images, and we
propose a few original definitions along with examples of their possible
use. The object delineation may be coarse, and this may have several

* Boundaries between objects can be imprecisely defined, leading in
handling fuzzy objects instead of crisp ones. Therefore, the measures
that will be defined need to apply for both crisp and fuzzy objects.
Another consequence is that topology is not reliable for recognition,
since a connected object in the map can be segmented in several parts
in the image, or on the contrary, two different objects may be not
separated in the segmented image.
* The objects may be only partially detected, which limits drastically
measures based only on size and shape of the objects.

In such cases, individual recognition of each object is almost impossible,
or would be unreliable. Therefore, the features used in the recognition
process have to make use of the spatial arrangement of the objects in the
scene. Indeed, spatial relationships may allow to recognize objects with
reference to other ones.

We distinguish two kinds of spatial relationships. Some of them are well
defined if the objects are crisp, like adjacency, inclusion or other set
relationships. But since they are highly sensitive to errors or imprecision
in segmentation, more useful measures can be obtained by fuzzifying these
concepts. We define such measures using fuzzification principles or direct
translation of binary equations into fuzzy ones. Other relationships are
inherently vague concepts, like relative position. Fuzzy definitions of such
relationships are then more consistent than crisp ones. We will detail the
example of relative position.