Curvature in Digital 2d Images

Kovalevsky, Vladimir

doi:10.1142/s0218001401001283

Cited by 25 publications

(28 citation statements)

References 7 publications

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“…Recent results [32] indicate that the theoretical limit of accuracy of determining curvature in digitized images could be as high as 40 %, and this should be kept in mind. Especially here where most neck widths are in the range of a few pixels only.…”

Section: Algorithm Robustnessmentioning

confidence: 99%

Automated measurement of sintering degree in optical microscopy through image analysis of particle joins

Nellros

Thurley

Jönsson

et al. 2015

Pattern Recognition

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In general terms, sintering describes the bonding of particles into a more coherent structure, where joins form between packed particles, usually as a result of heating. Characterization of sintering is an important topic in the fields of metallurgy, steel, iron ore pellets, ceramics, and snow for understanding material properties and material strength. Characterization using image analysis has been applied in a number of these fields but is either semi-automatic, requiring human interaction in the analysis, or based on statistical sampling and stereology to characterize the sample. This paper presents a novel fully automatic image analysis algorithm to analyze and determine the degree of sintering based on analysis of the particle joins and structure. Quantitative image analysis of the sintering degree is demonstrated for samples of iron ore pellets but could be readily applied to other packed particle materials. Microscope images of polished cross-sections of iron ore pellets have been imaged in their entirety and automated analysis of hundreds of images has been performed. Joins between particles have been identified based on morphological image processing and features have been calculated based on the geometric properties and curvature of these joins. The features have been analyzed and determined to hold discriminative power based on a statistical evaluation using the Welch t-test and display properties consistent with sintering theory and results from traditional pellet diameter measurements on the heated samples.

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Section: Algorithm Robustnessmentioning

confidence: 99%

Automated measurement of sintering degree in optical microscopy through image analysis of particle joins

Nellros

Thurley

Jönsson

et al. 2015

Pattern Recognition

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“…Coordinates of points in digital images are specified with a precision of about ±0.7 pixel. The author has demonstrated [9] that estimating the curvature with a precision of for example 10% is impossible for digital curves with the curvature radius less than 270 pixels because of not sufficient precision of the coordinates.…”

Section: Computing the Curvature Of Digital Curvesmentioning

confidence: 99%

“…The curvature may be calculated as the i nverse of the radius of a circle through three sub-pixel points. The optimal distance between the points must be calculated as a function of a coarse estimate of the expected curvature [9]. The precision of estimating the curvature is essentially higher than that of known methods.…”

Section: Computing the Curvature Of Digital Curvesmentioning

confidence: 99%

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Algorithms in Digital Geometry Based on Cellular Topology

Kovalevsky

2004

Lecture Notes in Computer Science

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Abstract. The paper presents some algorithms in digital geometry based on the topology of cell complexes. The paper contains an axiomatic justification of the necessity of using cell complexes in digital geometry. Algorithms for solving the following problems are presented: tracing of curves and surfaces, recognition of digital straight line segments (DSS), segmentation of digital curves into longest DSS, recognition of digital plane segments, computing the curvature of digital curves, filling of interiors of n-dimensional regions (n=2,3,4), labeling of components (n=2,3), computing of skeletons (n=2, 3).

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“…Worring's approach [1] is only relevant for edgels on a pixel-grid; Kovalevsky [3] recently extended this to edgels with sub-pixel accuracy, using his own edge-finder. However, both authors basically follow the assumption that curvature for low-curvature regions can be calculated more accurately than for high-curvature regions, since for the former smoothing will be less invasive than for the latter, and as a consequence concentrate on high-curvature regions with a radius of curvature below 40 pxl.…”

Section: Introductionmentioning

confidence: 99%

Error-Bounds on Curvature Estimation

Utcke

2003

Scale Space Methods in Computer Vision

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Abstract. Estimation of a digital curve's curvature at any given point is needed for many tasks in computer vision, be it differential invariants or curvature scale space. However, curvature estimation is known to be very susceptible to noise on the contour. We shall show how noise on the contour affects the relative accuracy of the curvature computation. One interesting result is that, contrary to intuition, the accurate calculation of the curvature for low-curvature regions is in fact impossible for common image-sizes, while reasonable results may under favourable conditions be obtained for higher-curvature regions.

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Curvature in Digital 2d Images

Cited by 25 publications

References 7 publications

Automated measurement of sintering degree in optical microscopy through image analysis of particle joins

Automated measurement of sintering degree in optical microscopy through image analysis of particle joins

Algorithms in Digital Geometry Based on Cellular Topology

Error-Bounds on Curvature Estimation

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