CURVE SHAPE MATCHING AND DIFFERENCE DETECTION
Jarmo Pirhonen
Institute of Photogrammetry and Remote Sensing
Helsinki University of Technology
Finland
Commission III, Working Group 2
KEY WORDS: Matching, Registration, Change Detection
ABSTRACT
A method for matching curves and detecting differences under rigid motion transformations is described. After least
squares matching the result for a difference detection purpose can be far from satisfactory. A method presented in
this paper use basic rigid motion invariants, distance, angle and dot product in a difference detection search process
after least squares matching.
. Shortly, main parts of the process are follows. First, a least squares match under rigid transformation is computed.
Second, for a one of the curves previously mentioned intra curve invariants are calculated and used later to extract
good local areas along the curve for final motion computation. Corresponding points from another curve are solved
using specified computations, the method does not extract any features there. The key idea is that when first curve
is deformed to another curve some parts of the first curve change less than another parts. Our process tries to detect
the less deformed parts and use those parts of a curve in a motion computation. A curve is represented as a B-spline
curve function and invariant features are computed from the coefficients of the that function not from the actual
curve points.
0. INTRODUCTION
Shape matching and difference detection are here
considered as problems that arise frequently in digital
close range photogrammetry or geometric computer
vision tasks. Typical examples are difference detection
between CAD-model and measured model or between
measured models which acquired at different times from
the same object or differences are needed between
different objects which have some similar geometric
parts.
Main assumption considered here is that difference
detection have to be done without corresponding control
information. So, the one side of the problem is matching
and another side is difference detection.
From the rigid motion transformation point of view
differences between models can considered as errors.
Papers by (Karras et al, 1993), (Pilgrim, 1991) and
(Zhang, 1994) have for example treated differences as
(gross) errors in iterative least squares matching prob-
lem. In every iteration (gross) errors are localized and
rejected from the next iteration round. Usually errors of
different size change the weight of an observation.
Problem leads to iterative weighting scheme, where not
only the parameters of the motion transformation are
iterated, but also the weights are iterated too. In this
paper we have not used iterative weighting in the least
squares estimation problem but it can be also used with
the presented method.
Differential features are commonly used in matching
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
problems. Geometric invariant features remain
unchanged under considered geometric transformation.
Usually features are extracted independently from each
data set and then the correspondences between these
invariant features are searched. We also use basic rigid
motion invariants, distance, angle, and dot product, but
a bit different way than usually.
1. B-SPLINE CURVES
We use parametric B-spline curve representation. Given
the knot sequence t,«t,«...«t,,,, a parametric non-rational
B-spline curve of order k (of degree k-1) with the end
points a-t, and b-t,,, can be represented as
C®=Y PB, © (1)
i=1
where t is the curve parameter.
P, is vector of the coefficients or guiding
points (dimension is degree of the curve).
B,,(t) are B-splines of order k, that can be
defined (and also computed efficiently) with
the recursive Cox-de Boor algorithm (de
Boor, 1978).
Here it can only bring to notice some important parts of
general problems that spline fitting includes. Good and
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