The authors wish to derive a shape representation technique that is useful for
shape recognition and comparison. In particular they focus on concisely
describing shapes based on curvature properties at various scales.
This paper presents a shape decomposition operation which simultaneously
performs data interpolation, data smoothing, and segmentation. Each
minimization operator has curvature tuning and a different spatial sensitivity
function, so the different possible descriptions capture curvature information
at multiple scales. These minimization operators are collectively called
curvature-tuned smoothing (CTS). The shape description method is
multiscale,
but the notion of scale is based on curvature-scale space rather than the
conventional definition in terms of Gaussian blurring and spatial frequency.
Two parameters must be specified when applying this technique:
Sampling grid for curvature space
Scalar value that determines relevance of the model set
The shape description technique presented in this paper has many advantages in
recognition of curved objects, including:
Objects which are similar but have no identical subcontours can still be
matched, unlike many existing methods
Noise is generally captured in the lower levels of the multiscale
representation as desired, so higher levels of similar shapes with different
types of noise still tend to match well
The method handles open curves, closed curves, and primitives from the
visible part of an occluded curve
Many natural objects can be described in one way; the CTS method allows
multiple ``good" representations of any single region
Curvature information is not corrupted by smoothing
The description is computed using local computations, so fast parallel
implementations seem possible
The CTS representation is applicable to recognition and matching
The method's main shortcoming is that it models objects as being locally
approximately circular or quadric in shape. For a wide range of smoothly
curved objects, this assumption seems appropriate. However for rough objects
this may be inappropriate.
Further issues to be explored include:
Complete development of CTS-based surface recognition
Inference of volumetric models from the curvature-based segments
Reconstruction of original data from CTS description