Preface

Rosenfeld, Azriel; Klette, Reinhard

doi:10.1016/b978-155860861-0/50000-6

Cited by 26 publications

(41 citation statements)

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“…The digital image data are processed with some threshold algorithms in order to obtain a contour of the object. The object contour is a base for different geometrical measurements (Klette and Rosenfeld [1]). …”

Section: Introductionmentioning

confidence: 99%

Length measurements in digital images by using an anchored discrete convolution algorithm

Suhadolnik¹,

Petriši²,

Kosel³

2009

WIT Transactions on the Built Environment

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A digital image could be used as a source of data for various dimensional measurements. After acquiring the digital image of the measured object, the object contour is determined. The contour is composed of a sequence of distinct pixels which contain centre points. This is a representation of a digital curve or digital arc from which the object length or the perimeter could be determined. In order to calculate the approximate length of the object, we introduce a new algorithm called an anchored discrete convolution. The algorithm is based on a discrete convolution by using different convolution masks and points anchored in the pixels. Unfortunately, the use of an ordinary convolution distorts the curve shape and introduces large errors in length calculation. In our case the anchoring limits the point shifting into the pixel area during the calculation of the curve length. In this paper different convolution masks are used on an experimental digital curve in order to evaluate the presented algorithm as a measuring tool. In addition, different real objects were optically scanned and the perimeters of the objects were determined from the acquired images.

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Section: Introductionmentioning

confidence: 99%

Length measurements in digital images by using an anchored discrete convolution algorithm

Suhadolnik¹,

Petriši²,

Kosel³

2009

WIT Transactions on the Built Environment

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“…However, in this publication, no math-ematical proof was given for linear run time or general correctness (i.e., that its solution iterates, for any simple cube-curve, to the MLP). This original rubberband algorithm is also published in the monograph [10]. Recent applications of this algorithm are in 3D medical imaging; see, for example, [6,22].…”

Section: Introductionmentioning

confidence: 99%

Shortest Paths in a Cuboidal World

Klette

2006

Lecture Notes in Computer Science

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Abstract. Since 1987 it is known that the Euclidean shortest path problem is NP-hard. However, if the 3D world is subdivided into cubes, all of the same size, defining obstacles or possible spaces to move in, then the Euclidean shortest path problem has a linear-time solution, if all spaces to move in form a simple cube-curve. The shortest path through a simple cube-curve in the orthogonal 3D grid is a minimum-length polygonal curve (MLP for short). So far only one general and linear (only with respect to measured run times) algorithm, called the rubberband algorithm, was known for an approximative calculation of an MLP. The algorithm is basically defined by moves of vertices along critical edges (i.e., edges in three cubes of the given cube-curve). A proof, that this algorithm always converges to the correct MLP, and if so, then always (provable) in linear time, was still an open problem so far (the authors had successfully treated only a very special case of simple cube-curves before). In a previous paper, the authors also showed that the original rubberband algorithm required a (minor) correction. This paper finally answers the open problem: by a further modification of the corrected rubberband algorithm, it turns into a provable linear-time algorithm for calculating the MLP of any simple cube-curve. The paper also presents an alternative provable linear-time algorithm for the same task, which is based on moving vertices within faces of cubes. For a disticntion, we call the modified original algorithm now the edgebased rubberband algorithm, and the second algorithm is the face-based rubberband algorithm; the time complexity of both is in O(m), where m is the number of critical edges of the given simple cube-curve.

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“…For information on Digital Topology we recommend the survey [11] and the books by Kong and Rosenfeld [12], and by Klette and Rosenfeld [9].…”

Section: Introductionmentioning

confidence: 99%

Deletion of (26,6)-Simple Points as Multivalued Retractions

Escribano

Giraldo

Sastre

2012

Computational Topology in Image Context

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Abstract. In a recent paper we have introduced a notion of multivalued continuity in digital spaces which extends the usual notion of digital continuity and allows to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points in 2-D, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we extend some of these results to 3-dimensional digital sets.

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Preface

Cited by 26 publications

References 0 publications

Length measurements in digital images by using an anchored discrete convolution algorithm

Length measurements in digital images by using an anchored discrete convolution algorithm

Shortest Paths in a Cuboidal World

Deletion of (26,6)-Simple Points as Multivalued Retractions

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