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3D distance fields: A survey of techniques and applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the ..."
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Cited by 74 (3 self)
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A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?
Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods
, 1999
"... We propose a new exact Euclidean distance transformation (DT) by propagation, using bucket sorting. A fast but approximate DT is first computed using a coarse neighborhood. A sequence of larger neighborhoods is then used to gradually improve this approximation. Computations are kept short by restric ..."
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Cited by 47 (6 self)
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We propose a new exact Euclidean distance transformation (DT) by propagation, using bucket sorting. A fast but approximate DT is first computed using a coarse neighborhood. A sequence of larger neighborhoods is then used to gradually improve this approximation. Computations are kept short by restricting the use of these large neighborhoods to the tile borders in the Voronoi diagram of the image. We assess the computational cost of this new algorithm and show that it is both smaller and less imagedependent than all other DTs recently proposed. Contrary to all other propagation DTs, it appears to remain o(n²) even in the worstcase scenario.
FAST AND EXACT SIGNED EUCLIDEAN DISTANCE TRANSFORMATION WITH LINEAR COMPLEXITY.
"... We propose a new signed or unsigned Euclidean distance transformation algorithm, based on the local corrections of the wellknown 4SED algorithm of Danielsson. Those corrections are only applied to a small neighborhood of a small subset of pixels from the image, which keeps the cost of the operation ..."
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Cited by 21 (3 self)
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We propose a new signed or unsigned Euclidean distance transformation algorithm, based on the local corrections of the wellknown 4SED algorithm of Danielsson. Those corrections are only applied to a small neighborhood of a small subset of pixels from the image, which keeps the cost of the operation low. In contrast with all fast algorithms previously published, our algorithm produces perfect Euclidean distance maps in a time linearly proportional to the number of pixels in the image. The computational cost is close to the cost of the 4SSED approximation. 1
Multiobject segmentation of brain structures in 3D MRI using a computerized atlas
, 1999
"... We present a hierarchical multiobject surfacebased deformable atlas for the automatic localization and identification of brain structures in MR images. The atlas is built as a multiobject set of 3D triangulated closed surfaces, each representing a given brain structure, and sharing its faces with ..."
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Cited by 13 (6 self)
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We present a hierarchical multiobject surfacebased deformable atlas for the automatic localization and identification of brain structures in MR images. The atlas is built as a multiobject set of 3D triangulated closed surfaces, each representing a given brain structure, and sharing its faces with neighboring structures. To support such a topology unambiguously, the multiobject mesh is build upon a Face Centered Cubic grid to maintain a unique kind of shared boundary elements. Hence, the voronoi neighborhoods of grid points are rhombic dodecahedra so that neighboring grid points always share a common face of a given size (cubic grid points can also share an edge or a corner). The registration of the atlas to a patient's MR image is done in two steps: a global registration based on the matching of the cortical surface and the ventricles followed by a multiobject active surface deformation to account for the local shape deformations. First, the cortical surface and the ventricular sy...
The case for approximate Distance Transforms
"... Starting with a binary raster, the calculation of exact Euclidean distance from the foreground pixels (1elements) to the background pixels (0elements) is a simple yet timeconsuming operation. Elsewhere it is argued that for some applications (such as pattern recognition and robotics for example) ..."
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Starting with a binary raster, the calculation of exact Euclidean distance from the foreground pixels (1elements) to the background pixels (0elements) is a simple yet timeconsuming operation. Elsewhere it is argued that for some applications (such as pattern recognition and robotics for example) the calculation of approximate Euclidean distance is a viable, quick and efficient alternative solution. There has been much research on a number of innovative approximate distance transforms. The vast majority of these have been reported in the computer science and mathematical literature, and yet given its inherent spatiality, the subject of distance does not appear in most GIS textbooks. This is surprising given the amount of research activity on approximate distance transforms over the last decade and its applicability to GIS. This paper reviews the major approximate distance calculation methods, establishing a case for their possible use in spatial science and suggesting future research directions.
Multidimensional Object Representation by a Parametric Deformable Model
, 1998
"... this paper, we present a parametric deformable model in the framework of multidimensional object modeling. Our model is expressed as hybrid ellipsoids suitable for both globally and locally deforming the reconstructed shape. This compact object representation is developed in the aim of a future mult ..."
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Cited by 2 (0 self)
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this paper, we present a parametric deformable model in the framework of multidimensional object modeling. Our model is expressed as hybrid ellipsoids suitable for both globally and locally deforming the reconstructed shape. This compact object representation is developed in the aim of a future multidimensional objectoriented image compression scheme, while easily providing a way to visualize the reconstructed object. This should make our model attractive for e.g. medical imaging, for which an object visualization is needed to help diagnosis as well as an efficient storage and archival capacity to improve remote access to the data. The focus is put on the definition of a suitable erroroffit criterion to assess the matching of our model to the data. According to this criterion, the model parameters are optimized by means of a genetic algorithm and compared with classical optimization techniques. The objects are assumed to be previously extracted from digital images, therefore providing an observation in the form of data points or a binary mask. Therefore the proposed modeling technique does not rely on a particular segmentation technique. Examples are given in this paper for manually generated synthetic contours, as well as myocardium contours automatically extracted from MRI datasets. Furthermore, the compact representation of the presented parametric modeling technique is compared to a stateoftheart 2D shape coding technique. We discuss in details the obtained modeling and coding results and propose an improvement of the method to recover more detailed shapes. This paper is organized as follows. In Sec. 2, we define the hybrid ellipsoid model, starting from the general hyperquadric primitives. Various erroroffit functions including distance evaluations are ...
OutofCore Distance Transforms
"... (a) Input CT image of an object (b) Distance field on the inside of the object (c) Distance field on the outside of the object Figure 1: The result of the OoCDT algorithm for an ”CylinderHead ” model (size: 850 × 800 × 1059 ≈ 700M cells). Note that the data size of the distance field is about 3GB ( ..."
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(a) Input CT image of an object (b) Distance field on the inside of the object (c) Distance field on the outside of the object Figure 1: The result of the OoCDT algorithm for an ”CylinderHead ” model (size: 850 × 800 × 1059 ≈ 700M cells). Note that the data size of the distance field is about 3GB (4 bytes/cell), which is too large to allocate to the RAM. Our algorithm can compute such large distance fields on common 32bit computers. This paper presents a method for computing distance fields from large volumetric models. Conventional methods have strict limits in terms of the amount of memory space available, as all volumetric models must be allocated to the random access memory (RAM) to compute distance fields. We resolve this problem through an outofcore strategy. Our algorithm starts by decomposing volumetric models into small regions known as clusters, and distance fields are then computed by Local Distance Transform (LDT) and InterCluster Propagation (ICP). LDT computes the distance transform for each cluster, and since it is independent, other clusters can also be saved to the storage medium. ICP propagates the distance at the boundary of the cluster to neighboring clusters to remove inconsistency in distance fields. In addition, we propose an efficient ordering algorithm based on the propagated distance to reduce LDT and ICP. This paper also demonstrates the results of distance transform from volumetric models with over a billion cells.
Euclidean Distance Task in an Picture Dealing Out Applications
"... Abstract In this paper, we can take advantage of using different distance functions in image processing Applications. The proposed Methods are based on wellknown algorithms that use Distance measurement. Our final purpose is to find the distance between two points in a single image using Euclidean ..."
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Abstract In this paper, we can take advantage of using different distance functions in image processing Applications. The proposed Methods are based on wellknown algorithms that use Distance measurement. Our final purpose is to find the distance between two points in a single image using Euclidean Distance function that provide the best results for a given problem, so we present some tools that help with finding them.
MODIFIED SEQUENTIAL ALGORITHM USING EUCLIDEAN DISTANCE FUNCTION FOR SEED FILLING 1 SAADIA SADDIQUE, 2
"... Euclidean Distance Transform has been widely studied in computational geometry, image processing, computer graphics and pattern recognition. Euclidean distance has been computed through different algorithms like parallel, linear time algorithms etc. On the basis of efficiency, accuracy and numerical ..."
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Euclidean Distance Transform has been widely studied in computational geometry, image processing, computer graphics and pattern recognition. Euclidean distance has been computed through different algorithms like parallel, linear time algorithms etc. On the basis of efficiency, accuracy and numerical computations, existing and proposed techniques has been compared. This study proposed a new technique of finding Euclidian distance using sequential algorithm. An experimental evaluation has shown that proposed technique has reduced the drawbacks of existing techniques. And the use of sequential algorithm scans has reduced the computational cost.
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"... header for SPIE use Multiobject segmentation of brain structures in 3D MRI using a computerized atlas ..."
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header for SPIE use Multiobject segmentation of brain structures in 3D MRI using a computerized atlas