Showing papers on "Distance transform published in 1999"

Distance transformations: fast algorithms and applications to medical image processing

Abstract: Medical image processing is a demanding domain, both in terms of CPU and memory requirements. The volume of data to be processed is often large (a typical MRI dataset requires 10 MBytes) and many processing tools are only useful to the physician if they are available as real-time applications, i.e. if they run in a few seconds at most. Of course, a large part of these demands are - and will be - handled by the development of more powerful hardware. On the other hand, when faced with non-linear computational complexity, the development of improved algorithms is obviously the best solution. Distance transformations, a powerful image analysis tool used in a number of problems such as image registration, requires such improvements. A distance map is an image where the value of each pixel is the distance from this pixel to the nearest pixel belonging to a given set or object. A distance transformation (DT) is an algorithm that computes a distance map from a binary image representing this set of pixels. This definition is global in the sense that it requires finding the minimum on a set of distances computed between all image pixels and all object pixels. Therefore, a direct application of the definition usually leads to an unacceptable computational complexity. Numerous algorithms have been proposed to localize this definition of distance to the nearest pixel and allow a faster DT computation, but up to now, none of them combines both exactness and linear complexity. Numerous applications of distance transformations to image analysis and pattern recognition have been reported and those related to medical image processing are explored in what follows. Chapter 1 introduces a few basic concepts, a typical application of distance transformations in pattern recognition and the key challenges in producing a DT algorithm. Chapter 2 contains an exhaustive critical review of published algorithms. The strong and weak points of the most popular ones are discussed and the core principles for our original algorithms are derived. Chapters 3, 5, 6, 8 and 10 present original distance transformation algorithms. Each of those chapters is organized in a somewhat similar fashion. First we describe the algorithm. Then we evaluate its computational complexity and compare it to the state of the art. Chapter 4, 7, 9 and 11 each present an application to a particular problem in medical image processing, using the algorithm developed in the previous chapter. Ideally, the description of any medical image processing problem should include a medical justification of the need for an automated processing, a complete review of the state of the art in the field, a detailed description of the proposed processing method, and an evaluation of the accuracy of the results and their medical significance. Because of both time and space constraints in this thesis, such an exhaustive work will only be presented for the application in chapter 4, while the other applications will be described more briefly. Chapter 3 describes a new exact Euclidean distance transformation using ordered propagation. It is based on a variation of Ragnelmam's approximate Euclidean DT. We analyze the error patterns for approximate Euclidean DT using finite masks, and we derive a rule defining, for any pixel location, the size of the neighborhood that guarantees the exactness of the DT. This algorithm is particularly well-suited to implement mathematical morphology operations, which are examined in details. In Chapter 4, we apply the algorithm of chapter 3 to the segmentation of neuronal fibers from microscopic images of the sciatic nerve. In particular, it is used to determine the thickness of the myelin sheath surrounding the center of the fiber. This study was carried out in collaboration with the Neural Rehabilitation Engineering Laboratory, UCL. Chapter 5 proposes another exact Euclidean distance transformation, based on the explicit computation of the Voronoi division of the image. Possible error locations are detected at the corners of the Voronoi polygons and corrected if needed. This algorithm is shown to be the fastest exact EDT to date. It approaches the theoretical optimal complexity, a CPU time proportional to the number of pixels on which the distance is computed. Chapter 6 investigates how the algorithms of chapters 3 and 5 can be extended to 3 dimensional images. It shows the limitations of both approaches and proposes an hybrid algorithm mixing the method of chapter 5 and Saito's. In Chapter 7, the 3D Euclidean DT is applied to the registration of MR images of the brain where the matching criterion is the distance between the surfaces of similar objects (skin, cortex, ventricular system, ...) in both images. Examples are shown, from projects with the Neuro-physiology Laboratory, UCL, and with the Positron Tomography Laboratory, UCL. Chapter 8 discusses an extension of the distance transformation concept: geodesic distances on non-convex domains. Because geodesic distances are based on the notion of paths, a trade-off has to be introduced between the accuracy with which straight lines are represented and the way curves of the domain are followed. It is shown that, whatever the trade-off chosen, there is an efficient implementation of the geodesic DT by propagation. By back-tracking the geodesic distance propagation, one can find the shortest path between a target and a starting point. In chapter 9, this is used to plan the optimal path for the camera movements in virtual endoscopy, a work done in collaboration with the Surgical Planning Laboratory, Harvard Medical School, Boston. Chapter 10 extends the Euclidean distance transformation from finding the nearest object pixel to finding the k nearest object pixels. It is shown that this can be done with a complexity increasing linearly with k. In Chapter 11, the k-DT is used as a fast implementation of the k Nearest Neighbors (k-NN) classification between different tissue types in multi-modal MR imaging. This is illustrated through the classification of multiple sclerosis lesions from T1-T2 images, provided by the Radiology unit, St-Luc Hospital, UCL, via the Positron Tomography Laboratory, UCL. Finally, a general conclusion is drawn. It reviews the main contributions of the thesis, its applications and explores some new domains in which their applications could also be useful. Ultimately, the publications related to this thesis are briefly reviewed.

The Earth Mover's Distance under transformation sets

Abstract: The Earth Mover's Distance (EMD) is a distance measure between distributions with applications in image retrieval and matching. We consider the problem of computing a transformation of one distribution which minimizes its EMD to another. The applications discussed here include estimation of the size at which a color pattern occurs in an image, lighting-invariant object recognition, and point feature matching in stereo image pairs. We present a monotonically convergent iteration which can be applied to a large class of EMD under transformation problems, although the iteration may converge to only a locally optimal transformation. We also provide algorithms that are guaranteed to compute a globally optimal transformation for a few specific problems, including some EMD under translation problems.

Detail-directed hierarchical distance fields

Abstract: A method generates a detail directed hierarchical representation of a distance field that is enclosed by a bounding box. The method begins by partitioning the bounding box enclosing the distance field into cells. Each cell has a size corresponding to detail of the distance field and a location with respect to the bounding box. Next, the distance field is sampled to obtain a set of values of the distance field for each cell. A method for reconstructing the portion of the distance field enclosed by the cell is specified for each cell. The location and size, the set of values, and the method for reconstructing for each cell are stored in a memory to enable reconstruction of the distance field by applying the reconstruction methods of the cells to the values.

Fast and exact signed Euclidean distance transformation with linear complexity

Abstract: We propose a new signed or unsigned Euclidean distance transformation algorithm, based on the local corrections of the well-known 4SED algorithm of Danielsson (1980). 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.

Line-based recognition using a multidimensional Hausdorff distance

Abstract: A line-feature-based approach for model based recognition using a four-dimensional Hausdorff distance is proposed. This approach reduces the problem of finding the rotation, scaling, and translation transformations between a model and an image to the problem of finding a single translation minimizing the Hausdorff distance between two sets of points in a four-dimensional space. The implementation of the proposed algorithm can be naturally extended to higher dimensional spaces to efficiently find correspondences between n-dimensional patterns. The method performance and sensitivity to segmentation problems are quantitatively characterized using an experimental protocol with simulated data. It is shown that the algorithm performs well, is robust to occlusion and outliers, and that it degrades nicely as the segmentation problems increase. Experiments with real images are also presented.

Reconstruction and simplification of surfaces from contours

Abstract: In this paper we consider the problem of reconstructing triangular surfaces from given contours. An algorithm solving this problem has to decide which contours of two successive slices should be connected by the surface (branching problem), and, given that, which vertices of the assigned contours should be connected for the triangular mesh (correspondence problem). We present a new approach that solves both tasks in an elegant way. The main idea is to employ discrete distance fields enhanced with correspondence information. This allows us not only to connect vertices from successive slices in a reasonable way but also to solve the branching problem by creating intermediate contours where adjacent contours differ too much. Last but not least we show how the 2D-distance fields used in the reconstruction step can be converted to a 3D-distance field that can be advantageously exploited for distance calculations during a subsequent simplification step.

Method for estimating volumetric distance maps from 2D depth images

Abstract: A volumetric distance map of an object is generated from one or more depth images of the object. Each depth image is projected onto the object by casting parallel rays to the object. The parallel rays are cast perpendicular to the depth image. Sample points in a projected distance volume represent distances from the distance map to a surface of the object. The magnitude of a local gradient at each sample point of the projected distance volume is determined, and each distance at each sample point is divided by the magnitude of the corresponding local gradient at each sample point to obtain a scalar distance to a closest surface of the object.

Representing a color gamut with a hierarchical distance field

Abstract: The invention provides a method for representing a device color gamut as a detail directed hierarchical distance field. A distance field representing the device color gamut is enclosed with a bounding box. The enclosed distance field is partitioned into a plurality of cells. Each cell has a size corresponding to detail of the continuous distance field and a location with respect to the bounding box. A set of values of the enclosed distance field is sampled for each cell. A method for reconstructing the portion of the distance field enclosed by the cell is specified. The size, the location, the set of values, and the method for reconstructing is stored in a memory to enable reconstruction of the device color gamut by applying the reconstruction methods of the cells to the values.

Matching for Shape Defect Detection

Abstract: The problem of defect detection in 2D and 3D shapes is analyzed. A shape is represented by a set of its contour, or surface, points. Mathematically, the problem is formulated as a specific matching of two sets of points, a reference one and a measured one. Modified Hausdorff distance between these two point sets is used to induce the matching. Based on a distance transform, a 2D algorithm is proposed that implements the matching in a computationally efficient way. The method is applied to visual inspection and dimensional measurement of ferrite cores. Alternative approaches to the problem are also discussed.1

Generation of tool paths for machining free-form pockets with islands using distance maps

Abstract: In this paper, we present a new procedure for generating tool paths using discrete distance maps, especially for dealing with free-form shaped pockets with multiple islands. In this procedure, a discrete distance map is computed by shading a right circular cone having the height of a given offset distance, while moving its apex along the boundary curve segments. Using the discrete distance maps, the proposed algorithm effectively extracts the characteristic points or the valid self-intersection points of offset curve segments. For an offset distance, one or more offset profiles are constructed without the topological problems by offsetting the boundary curve segments within the parameter values specified by these characteristic points, and connecting them into closed profiles using the topological information contained in the distance map. The gouging-free tool path is constructed by connecting these offset profiles, starting from the innermost offset profile. In the proposed method, we do not need any artificial bridges for a pocket with multiple islands to merge the pocket profile and the island profiles into a single boundary profile.

Computation of 3D curvatures on a wet snow sample

Abstract: The map of 3D curvatures of a porous medium characterizes most of its capillary properties. A model for directly computing curvatures from a three-dimensional image of the solid matrix of a porous medium is presented. A precise distance map of the object is built using the “chamfer” distance of discrete geometry. The set of local maxima of the distance map is used for quick location of the normal to each point P of the object's surface. The normal being known, principal radii of curvature are computed in 2D and lead to 3D curvature. This model was validated on geometric shapes of known curvature, then applied on a natural snow sample. The snow image was obtained from a serial cut (performed in cold laboratory) observed under specularly reflected light. Views of both fresh and sublimated sections were taken for each of the 64 section planes: this allowed easier distinction between snow and filling medium and made possible automatic contouring of section plane images. Curvature maps computed from pore and grain phases respectively were found to be in excellent agreement for each tested object shape, including the snow sample.

Method for detecting edges in an image signal

Abstract: An edge detection method employs binary morphological erosion. A binary image is generated from the gray-scale-value input image. A structure element is guided in a step-by-step manner across the binary image and generates an eroded binary image in accordance with an erosion rule. By forming the difference between the binary image and the eroded binary image, an output image containing the edges is generated. An output image which contains masked edges is generated through the use of a further erosion rule. The further erosion rule is based on a gray-scale value threshold and is applied to the eroded binary image to form a twice-eroded binary image. The difference between the twice-eroded binary image and the binary image forms the image which contains masked edges.

Method of searching database of three-dimensional protein structures

Abstract: A method of searching a database of three-dimensional protein structures. The method comprises the steps of setting a three-dimensional protein structure; forming a two-dimensional binary distance map based on the three-dimensional protein structure; forming a one-dimensional peripheral distribution based on the distance map; and comparing the one-dimensional peripheral distribution of a protein structure with that of another protein structure a dynamic programming algorithm. The method increases detection sensitivity and search speed.

B-Spline Surface Approximation to Cross-Sections Using Distance Maps

Abstract: The shape reconstruction of a 3D object from its 2D crosssections is important for reproducing it by NC machining or rapid prototyping In this paper, we present a method of surface approximation to cross-sections with multiple branching problems In this method, we first decompose each multiple branching problem into a set of single branching problems by providing a set of intermediate contours using distance maps For each single branching region, a procedure then performs the skinning of contour curves represented by cubic B-spline curves on a common knot vector, each of which is fitted to its contour points within a given accuracy In order to acquire a more compact representation for the surface, the method includes an algorithm for reducing the number of knots in the common knot vector The approximation surface to the crosssections is represented by a set of bicubic B-spline surfaces This method provides a smooth surface model, yet realises efficient data reduction

Surrounding environment recognizing device

Abstract: PROBLEM TO BE SOLVED: To provide a surrounding environment recognizing device capable of always exactly detecting an object in front without being affected by the color or size of the object. SOLUTION: Distance information detected by a laser range finder 1 is stored in a distance image memory 2 as a distance image in the arrangement of digital values, the distance image is vertically divided into small areas in the shape of strip in an arithmetic unit 4, an area, for which a vertical distance value is fixed and the value of correlation with a predetermined road model is less than a prescribed value concerning a relation between the distance and the vertical position of the distance image, in the distance image inside the divided small area is extracted as an object candidate area and when object candidate areas continuously exist, they are judged as one object candidate range so that a range, where the object exists, can be recognized. Therefore, since this device does not depend on the information of an edge as conventional one, the surrounding environment can be recognized without being affected by the color of the background or object.

Global Shape from Shading for an Endoscope Image

Abstract: Okatani and Deguchi [13] proposed a local Shape from Shading (SFS) method for endoscope images by assuming the point light, which is close to the projection center, to be at the projection center. We extended and modified their method and devised a global SFS algorithm for the reconstruction of the complex shape of an internal organ. Since the surface of an organ is not Lambertian in general, we obtained the bi-directional reflection distribution function (BRDF) curve by calibration using a robot arm to achieve accurate endoscope orientation and positioning. Inspired by the idea of Kimmel and Bruckstein [8], global SFS method is based on the identification of singular points on the distance map, which each has the surface normal pointing towards the light source. Equal distance contours are propagated from each singular point using a level set method to get a local distance map of the surface. This is repeated for all singular points. After that, a set of local distance maps are selected to be merged together to construct a global distance map using a new scheme. The shape of the object can then be obtained from the global distance map. Simulated and real experiments were performed to verify the algorithm. Experimental result of global SFS from a single real endoscope image of a human lung is quite good.

On Computing the Exact Euclidean Distance Transform on Rectangular and Hexagonal Grids

Abstract: In this paper we prove an equivalence relation between the distance transform of a binary image, where the underlying distance is based on a positive definite quadratic form, and the erosion of its characteristic function by an elliptic poweroid structuring element. The algorithms devised by Shih and Mitchell [18] and Huang and Mitchell [7], for calculating the exact Euclidean distance transform (EDT) of a binary digital image manifested on a square grid, are particular cases of this result. The former algorithm uses erosion by a circular cone to calculate the EDT whilst the latter uses erosion by an elliptic paraboloid (which allows for pixel aspect ratio correction) to calculate the square of the EDT. Huang and Mitchell‘s algorithm [7] is arguably the better of the two because: (i) the structuring element can be decomposed into a sequence of dilations by 3 × 3 structuring elements (a similar decomposition is not possible for the circular cone) thus reducing the complexity of the erosion, and (ii) the algorithm only requires integer arithmetic (it produces squared distance). The algorithm is amenable to both hardware implementation using a pipeline architecture and efficient implementation on serial machines. Unfortunately the algorithm does not directly transpose to, nor has a corresponding analogue on, the hexagonal grid (the same is also true for Shih and Mitchell‘s algorithm [7]). In this paper, however, we show that if the hexagonal grid image is embedded in a rectangular grid then Huang and Mitchell‘s algorithm [7] can be applied, with aspect ratio correction, to obtain the exact EDT on the hexagonal grid.

Fully Reversible Skeletonization for Volume Images Based on Anchor-Points from the D26 Distance Transform

Abstract: This paper presents a 3D (volume) surface skeletonization algorithm. Our algorithm uses iterative, topology preserving thinning guided by the D26 distance transform, which is the 3D equivalent of t ...

Device for measuring distance using stereographic picture

Abstract: PROBLEM TO BE SOLVED: To eliminate the reduction of distance measuring resolution in a long distance due to parallax that a picture element obtained through processing of a stereographic picture is set as a unit, and to improve the distance measuring resolution in a range from short distance to long distance. SOLUTION: A pair of pictures photographed by a stereoscopic camera 10 are processed by a stereo processing part 30 to calculate a distance of a city clock and obtain a correlation thereof every small area of the respective picture, and a stereo matching is performed to specify the corresponding small area and a displacement of the picture element (parallax) generating corresponding with a distance to an object is imaged as a distance data, thus generating a distance picture. Further, a recognition processing part 40 conducts stereo matching using both a reference picture and a comparison picture so as to obtain a parallax (sub pixel element) of one picture element or less, and a parallax that the picture element obtained from the distance picture is set as a unit is interpolated by a resolution of one picture element or less. Thus, the reduction of distance measuring resolution in a long distance can be eliminated and the accuracy of distance measurement in a range from short distance to long distance be also secured.

Distance distribution detector

Abstract: PROBLEM TO BE SOLVED: To reduce overhead and erroneous collation in image collation and distance calculation processing. SOLUTION: An image picked up from two cameras is digitized by an A/D converter. Next, the individual partial image of an analytic object is inputted to a collation means corresponding to each distance range to which it is expected to belong. Each collation means varies the resolution of an input image to collate a distance by spatial resolution necessary and sufficient to each distance range. Namely, each collation means converts the input image to an image of 2-n (n=0, 1, 2, 3) resolution in accordance with each corresponding distance range. As a resolution converting method, a method using the average of four adjacent pixels for halving the resolution is used. By constituting the distance distribution detector like this, data for post processing can be reduced and an arithmetic quantity can be reduced. Since collation is executed by spatial resolution corresponding to a distance, erroneous collation can also be reduced by this.

Random pattern generating device and its method, distance image generating device and its method, and program providing medium

Abstract: PROBLEM TO BE SOLVED: To provide a constitution capable of determining compatibility of a floodlight pattern image for distance measurement in a stereo-image method, and capable of generating a highly accurate distance image. SOLUTION: A floodlight pattern for three-dimensional shape measurement is evaluated by a pattern changing rate, a characteristic quantity, a dispersion value, pattern matching or the like, to determine the pattern, and thereby mismatching in inter-image correspondence or in distance image generation processing is removed to enable to generate the highly accurate distance image. A pattern changing rate, a characteristic quantity, or pattern matching is executed based on a photographed image of a measuring object on which the generated floodlight pattern is projected, to evaluate the photographed image. If the image is judged to be incompatible, generation of mismatching is suppressed in generation processing of the distance image by a feedback constitution for generating and floodlighting a new pattern, to thereby enable to generate the highly accurate distance image.

Calculating the Distance Map for Binary Sampled Data

Abstract: High quality rendering and physics-based modeling in volume graphics have been limited because intensity-based volumetric data do not represent surfaces well. High spatial frequencies due to abrupt intensity changes at object surfaces result in jagged or terraced surfaces in rendered images. Use of a distance-to-closest-surface function to encode object surfaces allows accurate reconstruction of objet surfaces for volumetric data. However, constructing the distance map for distance-based rendering requires a prior model of the object surface. Here we present a number of methods that can be used to estimate the distance map from a binary segmented volume, where no prior knowledge of object surfaces exists.

Object recognizing apparatus

Abstract: PROBLEM TO BE SOLVED: To recognize an object by clustering a window at high speed based on a label corresponding to a distance value calculated for the window SOLUTION: The image of an object picked up by image pickup means 3, 3' is converted through A/D converters 4, 4' and stored in image memories 5, 5' Image parts corresponding to a window are cut out from the image memories 5, 5' at an window cut out section 9 and delivered to a correlation calculating section 6 The correlation calculating section 6 performs correlation calculation from two cut out images and delivers a determined distance to a distance calculating section 7 A distance removing section 31 compares the measured distance with a predetermined estimation distance for each window and deletes a measured distance value from a distance memory section 8 A clustering section 33 performs clustering for a window having a measured distance which is not deleted at the distance removing section 31

Euclidean distance transform by stack filters

Abstract: Euclidean distance transform (EDT) using a gray-scale morphological erosion with a large distance structuring element is difficult to implement in real-time Herein, a stack filtering method that permits the implementation of EDT in real-time using only binary logic gates is proposed This letter reports a fast errorless method for EDT implementation