Related Work - Hierarchical Neural Networks for Image Interpretation - page 35

3. Related Work
In the previous chapter, we saw that object recognition in the human visual system
is based on a hierarchy of retinotopic feature maps with local recurrent connectiv-
ity. The following chapter reviews several applications of the concepts of hierarchy
and recurrence to the representation, processing, and interpretation of images with
computers.
3.1 Hierarchical Image Models
The world is hierarchical and so are images of it. Objects consist of parts and these
of subparts. Features can be decomposed into subfeatures all the way down to pixel
intensities. Thus, a visual scene can be represented at different degrees of abstrac-
tion.
Marr [153] was one of the first to propose analyzing visual stimuli at different
levels of abstraction. He proposed using local image operators to convert a pixel im-
age into a primal sketch. He suggested, for example, to use the zero-crossings of the
smoothed intensities's second derivative as edge detector. In Marr's approach to vi-
sion, the detected edges are grouped according to Gestalt principles [125] to produce
the full primal sketch. Adding other features, such as contour, texture, stereopsis,
and shading, yields a 2 2 D sketch. This representation is still viewer-centered and
describes properties of surface patches, such as curvature, position, depth, and 3D
orientation. Finally, a 3D representation is obtained. It is object-centered and con-
sists of volumetric primitives, generalized cones, organized as a hierarchy. Marr's
computational theory of vision has considerably inspired computer vision research.
However, its utility in practice has been limited by the use of symbolic representa-
tions which do not reflect ambiguities inherent in visual stimuli.
In the following sections, some subsymbolic hierarchical image representation
approaches are discussed. I group the different methods into generic signal decom-
positions, neural networks, and generative statistical models.
3.1.1 Generic Signal Decompositions
Some techniques decompose signals into a hierarchy of generic features, which are
efficient to compute and can be inverted. These decompositions are applicable to