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Describing Complicated Objects by Implicit Polynomials
January 1994 (vol. 16 no. 1)
pp. 38-53

This paper introduces and focuses on two problems. First is the representation power of closed implicit polynomials of modest degree for curves in 2-D images and surfaces in 3-D range data. Super quadrics are a small subset of object boundaries that are well fitted by these polynomials. The second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces. The attractive features of these polynomials for Vision is discussed.

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Index Terms:
polynomials; computer vision; image segmentation; image processing; curve fitting; complicated objects; implicit polynomials; representation power; closed implicit polynomials; 2-D images; surfaces; 3-D range data; super quadrics; object boundaries; noisy data; vision
D. Keren, D. Cooper, J. Subrahmonia, "Describing Complicated Objects by Implicit Polynomials," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 1, pp. 38-53, Jan. 1994, doi:10.1109/34.273718
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