Showing papers on "Distance transform published in 1988"

Finding local maxima in a pseudo-Euclidean distance transform

Abstract: Weighted distance transforms computed by using suitable integer weights are an adequate approximation to the Euclidean distance transform. In this paper, a criterion is introduced for identifying the local maxima in a specific weighted distance transform. The reverse weighted distance transformation is also introduced to associate a disc with every labeled pixel, and the discs centered on the local maxima are proved to be maximal discs.

The signed Euclidean distance transform and its applications

Abstract: The signed Euclidean distance transform described is a modified version of P.E. Danielsson's Euclidean distance transform (1980). The distance transform produces a distance map in which each pixel is a vector of two integer components. If a distance map is created inside the objects, the two integer values of a pixel in the distance map represent the displacements of the pixel from the nearest background point in the x and y directions, respectively. The unique feature of this distance transform, that a vector in the distance map is always pointing to the nearest background point, is exploited in several applications, such as the detection of dominant point in digital curves, curve smoothing, computing Dirichlet tessellations and finding convex hulls. >

A note on “distance transformations in digital images

Abstract: The influence of using distinct optimization criteria for determining the coefficients of a distance transform is studied. The criteria studied are (1) minimizing the maximum of the absolute value of the difference between the distance transform and Euclidaan distance, and (2) minimizing the root-mean-square difference between the distance transform and Euclidean distance. By allowing an overall scaling factor to have other than integer values, other integer approximations of the distance transform's coefficients result as optimal. Emphasis is given to isotropy, or invariance with respect to rotation, and to the use of unbiased distance estimates.

Method and apparatus for obtaining an object image and distance data of a moving object

Abstract: An apparatus for monitoring a moving object comprises an image memory for storing a reference monitor image of a designated monitor region, a distance map memory for storing a distance map, the monitor image of the designated monitor region and the distance map comprising a plurality of blocks having distance data from a predetermined reference point in the monitor region to points corresponding to the blocks, an object image detector for detecting an object image based on an input monitor image of the designated monitor region and the reference monitor image read out from the image memory, and a distance detector for detecting a distance from the reference point to the moving object in accordance with the detected object image and the distance map read out from the distance map memory.

An algorithm for a generalized distance transformation based on Minkowski operations

Abstract: A generalized distance transformation of binary images based on successive Minkowski operations is discussed. This distance transformation is obtained by using a two-scan algorithm. A related medial axis for image compression is defined. As an example of the transformation's application, a fast algorithm for elementary morphological operations with an arbitrary structuring element is given. >

Skeletonizing the distance transform on the hexagonal grid

Abstract: An efficient skeletonizing algorithm is presented for the hexagonal grid. The skeleton has unit width, except at crossings and in regions of the shape having even width. Otherwise the skeleton has all the properties generally required for correct skeletons. It includes all local maxima, so complete recovery of the original shape is obtained by using the reverse distance transformation. The algorithm uses only local operations. Thus it can be performed both on sequential and parallel computers. In the sequential case described only three passes through the image are necessary, two to compute the distance transform and one for the identification of skeletal pixels. >

Automated fast recognition and location of arbitrarily shaped objects by image morphology

Abstract: Morphological operations are used for segmentation, feature generation and location extraction. A recursive adaptive thresholding algorithm transforms a gray-level image into a set of multiple level regions of objects. A distance transformation algorithm then is used to transform a binary image into the minimum distance from each object point to the object's boundary. This algorithm uses a morphological erosion with a large structuring element which may correspond to Euclidean, city-block, or chessboard distance measures. A shape library database with hierarchical features is automatically generated. The features extracted are the shape number and the skeletal local-maximum points radii and coordinates. Object recognition is achieved by comparing the shape number and the hierarchical radii. Object location is detected by a hierarchical morphological bandpass filter. >

Industrial parts recognition and inspection by image morphology

Abstract: Application algorithms for industrial parts and tool recognition and inspection by image morphology techniques are discussed. A recursive adaptive thresholding algorithm transforms a gray-level image into a set of multiple-level regions of objects. This algorithm uses a morphological erosion with a large symmetrical concave structuring element. A distance-transformation algorithm transforms these binary image regions into the minimum distance from each object point to the boundary of the object. This algorithm also uses a morphological erosion. From the distance transform, it is possible to compute a shape number and extract the skeleton, which is useful for generic pattern recognition and feature extraction. Corner angles and the radii of circular holes can be located, identified, and estimated by using morphological openings and erosions. The algorithms allow robust tool and part recognition and inspection. >

Weighted Distance Transforms: A Characterization

Abstract: In many instances, it is convenient to label the space enclosed within the contour of a single-valued digital figure F. Labeling F by means of its distance transform DT, has been one of the first approaches to give structure to an otherwise amorphous space, and has been useful to reveal some of its features, especially those dependent on shape. In this framework, the set of the local maxima present in the DT plays a crucial role. In fact, the local maxima are necessary to identify the medial axis of F /1/. Moreover, figure decomposition techniques can be derived by suitably grouping the discs associated with the local maxima /2/.

Skeletonization And Distance Transformation By Greyscale Morphology

Abstract: Mathematical morphology applied to image processing which deals directly with shape is a more direct and faster approach to feature measurements than traditional techniques. It has grown to include many applications and architectures in image analysis. Binary morphology has been successfully extended to greyscale morphology which allows a new set of applications. In this paper, the distance transformation, skeletonization, and reconstruction algorithms using the greyscale morphology approach are described and proven to be remarkably simple. The distance transformation of an object is the minimum distance from inner points to the background of an object. The algorithm is a recursive greyscale erosion of the image with a small size structuring element. The distance can be Euclidean, chessboard, or city-block distance which depends on the selection of its structuring element. The skeleton extracted is the Medial Axis Transformation (MAT) which is produced from the result of the distance transformation. The values of the distance transform along the skeleton are maintained to represent distance to the closest boundary. We can easily reconstruct the distance transform from the skeleton by iterative greyscale dilations with the same struc-turing element. In order for this method to be useful for grey level images, a simple adaptive threshold algorithm using greyscale ero-sion with a non-linear structuring element has been developed.21 A decomposition technique which reduces the large size non-linear structuring element into a recursive operation with a small window allows real-time implementation.

Computing quadtree medial axis transform by a multi-layered pyramid of LISP-processor arrays

Abstract: The authors explore the potential of using the quadtree image-representation scheme in a multiprocessor pyramid and present algorithms for computing the quadtree medial-axis transform of a binary image on the basis of a bottom-up multilayered pyramid of LISP-processor arrays. All the data structures are represented in the list form. There are three layers of processors at each level of the pyramid: PYRAMID layer, DIST layer, and QMAT layer. The first two layers form the quadtree data structure and compute the chess-board distance transform values, and the QMAT layer computes the quadtree medial-axis transform. >

Skeletonizing The Distance Transform Parallelwise

Abstract: An iterated parallel algorithm to get the labeled skeleton of a digital figure F is presented. At every iteration, the current 8-connected contour is identified and the pixels preventing contour simplicity are taken as the skeletal pixels. The set of the skeletal pixels has all the properties generally satisfied by the skeleton, except for unit width. This property is enjoyed if one iteration of a standard parallel thinning algorithm is applied. Every skeletal pixel is assigned a label indicating the first iteration of the process at which it has been recognized as a skeletal pixel. Such a label is equal to the 4-distance of the pixel from the complement of F. The obtained labeled skeleton coincides with the skeleton one could get by skeletonizing the 4-distance transform of F.

On the hexagonal grid

Abstract: The hexagonal grid is a reasonable approximation of the human vision grid, is more suited to natural scenes than the square grid and avoids the 4neigbor/8-neighbor problem. Skeletons are good representations of digital shapes, and can be used for storage and shape editing. We compute efficient skeletons on the hexagonal distance transform. The computations can be performed either in parallel or sequentially, since only local operations are used.