Digitized circular arcs: characterization and parameter estimation

Worring, Marcel; Smeulders, A.W.M.

doi:10.1109/34.387505

Cited by 47 publications

(21 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[15], and errors occur if the window size is not locally adequate. Moreover, the accuracy of previously reported methods is not uniformly satisfactory [14][15][16]. We devised a multiplewindow curve fitting algorithm for digital curvature estimation leading to very accurate results and robust to signal variations and noise.…”

Section: Multiple-scale Fibre-level Features Extractionmentioning

confidence: 99%

“…Recent results indicate that the number of inflection points (at which the sign of the curvature changes) and curvature along the fibre or vessel are relevant tortuosity definitions [13], hence we include them in our dictionary of features. Accurate curvature estimation from samples is a well-known tricky task [14][15][16]. Two main issues are window size selection and accuracy.…”

Section: Multiple-scale Fibre-level Features Extractionmentioning

confidence: 99%

See 1 more Smart Citation

Tortuosity classification of corneal nerves images using a multiple-scale-multiple-window approach

Annunziata

Kheirkhah

Aggarwal

et al. 2014

Proceedings of the Ophthalmic Medical Image Analysis First International Workshop

View full text Add to dashboard Cite

Abstract. Classify in vivo confocal microscopy corneal images by tortuosity is complicated by the presence of variable numbers of fibres of different tortuosity level. Instead of designing a function combining manually selected features into a single coefficient, as done in the literature, we propose a supervised approach which selects automatically the most relevant combination of shape features from a pre-defined dictionary. To our best knowledge, we are the first to consider features at different spatial scales and show experimentally their relevance in tortuosity modelling. Our results, obtained with a set of 100 images and 20 fold cross-validation, suggest that multinomial logistic ordinal regression, trained on consensus ground truth from 3 experts, yields an accuracy indistinguishable, overall, from that of experts when compared against each other.

show abstract

Section: Multiple-scale Fibre-level Features Extractionmentioning

confidence: 99%

Section: Multiple-scale Fibre-level Features Extractionmentioning

confidence: 99%

Tortuosity classification of corneal nerves images using a multiple-scale-multiple-window approach

Annunziata

Kheirkhah

Aggarwal

et al. 2014

Proceedings of the Ophthalmic Medical Image Analysis First International Workshop

View full text Add to dashboard Cite

show abstract

“…In the space that is dual to the parameters space, a plane separating two sets of n 3D points is searched using tools coming from computational geometry [22]. In [18,9,14,27,23] a 2D point belonging to the intersection of n 2 half-planes is searched in the original plane using either brute-force algorithms [9,14,27] or tools coming from computational geometry [18,23].…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

Analytical Description of Digital Circles

Andrès

Roussillon

2011

Discrete Geometry for Computer Imagery

View full text Add to dashboard Cite

show abstract

“…On the other side, the digital circles and the digital circular arcs are on of the basic objects considered in image processing and shape analys. For more results we refer to [4].…”

Section: How Efficiently An Original Circle Can Be Reconstructed Frommentioning

confidence: 99%

The Discrete Moments of the Circles

Žunić

1999

Discrete Geometry for Computer Imagery

View full text Add to dashboard Cite

Abstract. The moment of (p, q)-order, mp,q(C), of a circle C given by (x − a) 2 + (y − b) 2 ≤ r 2 , is defined to be C x p y q dxdy. It is naturally to assume that the discrete moments dmp,q(C), defined ascan be a good approximation for mp,q(C). This paper gives an answer what is the order of magnitude for the difference between a real moment mp,q(C) and its approximation dmp,q(C), calculated from the corresponding digital picture. Namely, we estimatein function of the size of the considered circle C and its center position if p and q are assumed to be integers. These differences are upper bounded11 +ε , where ε is an arbitrary small positive number. The established upper bound can be understood as very sharp. The result has a practical importance, especially in the area of image processing and pattern recognition, because it shows what the picture resolution should be used in order to obtain a required precision in the parameter estimation from the digital data taken from the corresponded binary picture. 1

show abstract

Digitized circular arcs: characterization and parameter estimation

Cited by 47 publications

References 32 publications

Tortuosity classification of corneal nerves images using a multiple-scale-multiple-window approach

Tortuosity classification of corneal nerves images using a multiple-scale-multiple-window approach

Analytical Description of Digital Circles

The Discrete Moments of the Circles

Contact Info

Product

Resources

About