Shape description using cubic polynomial Bezier curves

Cinque, Luigi; Levialdi, S.; Malizia, Alessio

doi:10.1016/s0167-8655(98)00069-5

Cited by 39 publications

(56 citation statements)

References 2 publications

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“…Cubic BC was used for shape description in [2], with an a priori number of curve segments (segment rate-SR) each with the same number of contour points. The CP for the segments were determined as in [2] and for comparative purposes, the experiments used the same set of CP for the BC, QBC and QBC-n.…”

Section: B Comparative Results As a Shape Descriptormentioning

confidence: 99%

“…The CP for the segments were determined as in [2] and for comparative purposes, the experiments used the same set of CP for the BC, QBC and QBC-n.…”

Section: B Comparative Results As a Shape Descriptormentioning

confidence: 99%

“…While their origin can be traced back to the design of car body shapes in the automobile industries, their usage is no longer confined to this field. Indeed, their robustness in curve representation means BC now pervades many areas of multimedia technology, including shape description of characters [1] and objects [2], shape coding and error concealment for MPEG-4 coded objects [3].…”

Section: Introductionmentioning

confidence: 99%

“…This was the motivation behind this research, namely to reduce the gap between the curve and its control polygon without increasing the number of CP. Such an objective mandates an augmentation to the fundamental theoretical basis of the BC, which this paper addresses by introducing two novel BC enhancements 2 2 The preliminary idea behind this work was presented at IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2005) , namely quasi-Bezier curves (QBC), theory which considers local information within the classical BC framework, without any increase in either the number of CP or computational complexity incurred. It is especially noteworthy that QBC can be seamlessly integrated into all Bezier variants including the aforementioned degree elevation, composite and subdivision techniques, while concomitantly retaining all the central properties of the BC.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-Bezier curves integrating localised information

Sohel

Karmakar

Dooley

et al. 2008

Pattern Recognition

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Bezier curves (BC) have become fundamental tools in many challenging and varied applications, ranging from computer aided geometric design to generic object shape descriptors. A major limitation of the classical Bezier curve however, is that only global information about its control points (CP) is considered, so there can often be a large gap between the curve and its control polygon, leading to large distortion in shape representation. While strategies such as degree elevation, composite BC, refinement and subdivision reduce this gap, they also increase the number of CP and hence bit-rate, and computational complexity. This paper presents novel contributions to BC theory, with the introduction of quasi-Bezier curves (QBC), which seamlessly integrate localised CP information into the inherent global Bezier framework, with no increase in either the number of CP or order of computational complexity. QBC crucially retains the core properties of the classical BC, such as geometric continuity and affine invariance, and can be embedded into the vertex-based shape coding and shape descriptor framework to enhance rate-distortion performance. The performance of QBC has been empirically tested upon a number of natural and synthetically shaped objects, with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical BC and other established BC-based shape descriptor methods.

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Section: B Comparative Results As a Shape Descriptormentioning

confidence: 99%

“…The CP for the segments were determined as in [2] and for comparative purposes, the experiments used the same set of CP for the BC, QBC and QBC-n.…”

Section: B Comparative Results As a Shape Descriptormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quasi-Bezier curves integrating localised information

Sohel

Karmakar

Dooley

et al. 2008

Pattern Recognition

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show abstract

“…In particular, their robustness in curve and surface representation means they pervade many fields of multimedia technology including shape description of characters [1,2] and objects [3], active shape lip modelling (ASLM) [4], shape error concealment for MPEG-4 objects [5] and surface mapping [6]. The classical BC is defined by a set of control points (CP) with the number and orientation of these points governing the overall size and shape of the curve.…”

Section: Introductionmentioning

confidence: 99%

Bezier curve-based generic shape encoder

et al. 2010

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Existing Bezier curve-based shape description techniques primarily focus upon determining a set of pertinent control points (CP) to represent a particular shape contour. While many different approaches have been proposed, none adequately consider domain-specific information about the shape contour like its gradualness and sharpness, in the CP generation process which can potentially result in large distortions in the object's shape representation. This study introduces a novel Bezier curve-based generic shape encoder (BCGSE) that partitions an object contour into contiguous segments based upon its cornerity, before generating the CP for each segment using relevant shape curvature information. In addition, although CP encoding has generally been ignored, BCGSE embeds an efficient vertex-based encoding strategy exploiting the latent equidistance between consecutive CP. A non-linear optimisation technique is also presented to enable the encoder is automatically adapt to bit-rate constraints. The performance of the BCGSE framework has been rigorously tested on a variety of diverse arbitrary shapes from both a distortion and requisite bitrate perspective, with qualitative and quantitative results corroborating its superiority over existing shape descriptors.

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Image Analysis and Computer Vision: 1998

Rosenfeld

1999

Computer Vision and Image Understanding

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This paper presents a bibliography of over 2250 references related to computer vision and image analysis, arranged by subject matter. The topics covered include computational techniques; feature detection and segmentation; image and scene analysis; two-dimensional shape; pattern; color and texture; matching and stereo; three-dimensional recovery and analysis; three-dimensional shape; and motion. A few references are also given on related topics, including geometry and graphics, compression and processing, sensors and optics, visual perception, neural networks, artificial intelligence and pattern recognition, as well as on applications.

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Shape description using cubic polynomial Bezier curves

Cited by 39 publications

References 2 publications

Quasi-Bezier curves integrating localised information

Quasi-Bezier curves integrating localised information

Bezier curve-based generic shape encoder

Image Analysis and Computer Vision: 1998

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