3 research outputs found
Scale-based surface understanding using diffusion smoothing
The research discussed in this thesis is concerned with surface understanding from the
viewpoint of recognition-oriented, scale-related processing based on surface curvatures and
diffusion smoothing. Four problems below high level visual processing are investigated:
1) 3-dimensional data smoothing using a diffusion process;
2) Behaviour of shape features across multiple scales,
3) Surface segmentation over multiple scales; and
4) Symbolic description of surface features at multiple scales.
In this thesis, the noisy data smoothing problem is treated mathematically as a boundary
value problem of the diffusion equation instead of the well-known Gaussian convolution,
In such a way, it provides a theoretical basis to uniformly interpret the interrelationships
amongst diffusion smoothing, Gaussian smoothing, repeated averaging and
spline smoothing. It also leads to solving the problem with a numerical scheme of unconditional
stability, which efficiently reduces the computational complexity and preserves the
signs of curvatures along the surface boundaries.
Surface shapes are classified into eight types using the combinations of the signs of
the Gaussian curvature K and mean curvature H, both of which change at different scale
levels. Behaviour of surface shape features over multiple scale levels is discussed in
terms of the stability of large shape features, the creation, remaining and fading of small
shape features, the interaction between large and small features and the structure of
behaviour of the nested shape features in the KH sign image. It provides a guidance for
tracking the movement of shape features from fine to large scales and for setting up a surface
shape description accordingly.
A smoothed surface is partitioned into a set of regions based on curvature sign
homogeneity. Surface segmentation is posed as a problem of approximating a surface up
to the degree of Gaussian and mean curvature signs using the depth data alone How to
obtain feasible solutions of this under-determined problem is discussed, which includes the
surface curvature sign preservation, the reason that a sculptured surface can be segmented
with the KH sign image alone and the selection of basis functions of surface fitting for
obtaining the KH sign image or for region growing.
A symbolic description of the segmented surface is set up at each scale level. It is
composed of a dual graph and a geometrical property list for the segmented surface. The
graph describes the adjacency and connectivity among different patches as the
topological-invariant properties that allow some object's flexibility, whilst the geometrical
property list is added to the graph as constraints that reduce uncertainty. With this organisation,
a tower-like surface representation is obtained by tracking the movement of
significant features of the segmented surface through different scale levels, from which a
stable description can be extracted for inexact matching during object recognition
PERCEPTUAL ORGANIZATION AND THE CURVE PARTITIONING PROBLEM*
A basic attribute of the human visual system is its ability to group elements of a perceived scene or visual field into meaningful or coherent clusters; in addition to clustering o