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Pose estimation and object identification using complex algebraic representations
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DOI：10.1007/BF01259367.png)
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Abstract
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The comparison and alignment of two similar objects is a fundamental problem in pattern recognition and computer vision that has been considered using various approaches. In this work, we employ a complex representation for an algebraic curve, and illustrate how the algebraic transformation which relates two Euclidean equivalent curves can be determined using this representation. The idea is based on a complex representation of 2D points expressed in terms of the orthogonal x and y variables, with rotations of the complex numbers described using Euler's identity. We develop a simple formula for integer multiples of the rotation angle of the Euclidean transformation in terms of the real coefficients of implicit polynomial equations that are used to model 2D free form objects. When there is a translation, it can be determined using some new results on the conic-line factors of implicit polynomial curves. Experimental results are presented for data sets characterised by both noisy and missing data points to illustrate and validate our procedures.
Keywords:
absolute invariants
complex representations
Euclidean transformations
Fourier descriptors
implicit polynomial curves
noisy and missing data sets
object recognition and alignment
pose estimation
scatter matrix
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1.9K
Citations:
1.9K
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