Showing papers on "Distance transform published in 1993"

Comparing images using the Hausdorff distance

Abstract: The Hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa. Thus, this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. Efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model are presented. The focus is primarily on the case in which the model is only allowed to translate with respect to the image. The techniques are extended to rigid motion. The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. It is shown that the method extends naturally to the problem of comparing a portion of a model against an image. >

Global and local document degradation models

Abstract: Two sources of document degradation are modeled: i) perspective distortion that occurs while photocopying or scanning thick, bound documents, and ii) degradation due to perturbations in the optical scanning and digitization process: speckle, blurr, jitter, thresholding. Perspective distortion is modeled by studying the underlying perspective geometry of the optical system of photocopiers and scanners. An illumination model is described to account for the nonlinear intensity change occuring across a page in a perspective-distorted document. The optical distortion process is modeled morphologically. First, a distance transform on the foreground is performed, followed by a random inversion of binary pixels where the probability of flip is a function of the distance of the pixel to the boundary of the foreground. Correlating the flipped pixels is modeled by a morphological closing operation. >

A Strategy for Automated Multimodality Image Registration Incorporating Anatomical Knowledge and Imager Characteristics

Abstract: This paper describes two methods for automating registration of 3D medical images acquired from different modalities. One uses dispersion in an intensity based feature space as a measure of mis-registration, together with knowledge of imager characteristics. The other uses anatomical knowledge of proximity and containment between associated structures to modify a distance transform for registration. Pre-registered training images are used to customise the algorithms for specific applications. Using stochastic optimisation techniques, we automatically registered MR and CT images of the head from three patients using one training set. In each case, the accuracy of registration was comparable to that obtained by point landmark registration. We present initial results for the modified distance transform in the same clinical application, and in a new application to combine angiographic data with the surface of the brain derived from MR.

Matching 3D anatomical surfaces with nonrigid deformations using octree splines

Abstract: This paper presents a new method for determining the minimal non-rigid deformation between two 3-D surfaces, such as those which describe anatomical structures in 3-D medical images. Although we match surfaces, we represent the deformation as a volumetric transformation. Our method performs a least squares minimization of the distance between the two surfaces of interest. To quickly and accurately compute distances between points on the two surfaces, we use a precomputed distance map represented using an octree spline whose resolution increases near the surface. To quickly and robustly compute the deformation, we use a second octree spline to model the deformation function. The coarsest level of the deformation encodes the global (e.g., affine) transformation between the two surfaces, while finer levels encode smooth local displacements which bring the two surfaces into closer registration. We present experimental results on both synthetic and real 3-D surfaces.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Binary and grey-value skeletons: Metrics and algorithms

Abstract: A metric defines the distance between any two points. The “natural” metrics of the digital world do not approximate the Euclidean metric of the continuous world well. Skeletonization (sometimes named topology preserving shrinking or homotopic thinning) is one example in which this leads to unacceptable results. In the present work we propose and demonstrate skeletonization using path-based metrics which are a better approximation of the Euclidean metric. Moreover, we achieve a good performance on sequential processors by processing each pixel only once in the calculations of binary (Hilditch) and grey-value (upper) skeletons.

Subpixel distance maps and weighted distance transforms

Abstract: An algorithm for computing the Euclidean distance from the boundary of a given digitized shape is presented. The distance is calculated with sub-pixel accuracy. The algorithm is based on an equal distance contour evolution process. The moving contour is embedded as a level set in a time varying function of higher dimension. This representation of the evolving contour makes possible the use of an accurate and stable numerical scheme, due to Osher and Sethian.

Environment recognizing system based on image processing

Abstract: PURPOSE:To allow the easy and correct recognition of the three-dimensional conditions of an object with respect to an imaging section by synthesizing a focal distance data, an image signal data read out from a memory section and a distance data of a specific position thereby forming an image information data. CONSTITUTION:Position in an image formed on a screen based on a corresponding image signal data is specified for each part of a sorted image signal data. A focal point control section then controls a focal point adjusting mechanism to match the focal point of an optical system 13 at an imaging section 12 with a specific position of an object corresponding to thus specified position. At that time, focal distance of the optical system 13 at the time of matching the focal point with the specific position of the object, i.e., a focal distance data representative of the distance from the imaging section 12 to the specific position of the object, is obtained. The focal distance data is synthesized with the image signal data and the distance data relevant to a specific position thus forming an image information data.

DCT image fidelity metric and its application to a text-based scheme for image display

Abstract: The discrete cosine transform (DCT) can be used to transform two images into a space where it is easy to obtain an estimate of their perceptual distance. We used this method to find the closest fit of the ASCII symbols (which includes the English alphabet, numbers, punctuation, and common symbols) to rectangular segments of a gray-scale image. Each segment was converted into a DCT coefficient matrix which was compared to the coefficient matrix of each ASCII symbol. The image segment was replaced with the symbol that had the least weighted Euclidean distance. Thus, a page of text was generated that resembled the original image. The text image format has the advantage that it can be displayed on a non-graphic terminal or printer. It can also be sent via electronic mail without requiring further processing by the receiver. The processing scheme can also be used to preview stored images when transmission bandwidth is limited or a graphic output device is unavailable.

Solving city block metric and digital geometry problems on the BSR model of parallel computation

Abstract: in this paper we solve several geometric and image problems using the BSR (broadcasting with selective reduction) model of parallel computation. All of the solutions presented are constant time algorithms. The computational geometry problems are based on city block distance metrics: all nearest neighbors and furthest pairs of m points in a plane are computed on a two criteria BSR with m processors, the all nearest foreign neighbors and the all furthest foreign pairs of m points in the plane problems are solved on three criteria BSR with m processors while the area and perimeter of m iso-oriented rectangles are found on a one criterion BSR with m 2 processors. The problems on an nxn binary image which are solved here all use BSR with n 2 processors and include: histogramming (one criterion), distance transform (one criterion), medial axis transform (three criteria) and discrete Voronoi diagram of labeled images (two criteria).

Image encoding device and decoding device

Abstract: PURPOSE: To provide the binary image encoding device which generates an extremely small information amount and the binary image decoding device which obtains an output having a small error as to an original binary image. CONSTITUTION: The binary image encoding device has a binary image reducer unit 8 which reduces a binary image, a binary image encoder 16 which encodes the binary image, an outline extractor unit 12 which extracts an outline from the binary image, a curve generator 13 which generates a curve on the basis of the outline, a comparator 14 which compares the generated curve with the outline of the input binary image, and a corrector 10 which partially corrects the reduced binary image according to the comparison result of the comparator. The binary image decoding device has a binary image decoder 19 which restores the binary image, a binary image expander 20 which expands the binary image, an outline extractor 21 which extracts an outline from the binary image, a curve generator 22 which generates a curve on the basis of the outline, and a corrector 23 which corrects the binary image on the basis of the curve. COPYRIGHT: (C)1995,JPO

Skeletonisation as model-based feature detection

Abstract: Two closely related methods for skeletonisation via a Euclidean distance transform are presented. First from an observation on the response of the human visual system to a grey level image of the transform, convolution with the Marr-Hildreth operator is proposed. Secondly, it is suggested that skeletonisation can be performed by convolution of the distance transform with a function designed to detect the occurrence of a specific geometric model, or feature, in a way similar to that used in contemporary edge detection algorithms. Examples of the technique are shown and the results discussed.

Shape features in distance transforms

Abstract: Shape features characterizing patterns represented by their distance transform are illustrated. The role they can play in pattern decomposition is described with reference to a process based on the detection of a number of pixels significant for shape interpretation. Suitable sets of these pixels are regarded as feature sets, and used as seeds to be expanded into regions. After a merging phase, the regions originate a meaningful decomposition.

Picture area extracting device

Abstract: PURPOSE:To exactly separate and extract a desired picture from a background even in an area of a picture where a background color and a color coexist by expressing the area by plural reference vectors. CONSTITUTION:2N pieces of clustering modules 108-113 are assigned by each N piece for expressing the reference vectors of an objective area to be extracted, and the reference vectors of a background area. A control circuit 107 scans a reading circuit 106 so that the picture vectors of entire picture elements can be sequentially read out from a frame memory 105. The read picture vectors are transmitted to the modules of the objective area to be extracted, and the modules of the background area, a distance is calculated in parallel, and each minimum distance is stored in distance map memories 116 and 117. Then, an in-area picture element reading circuit 118 compares the distance to the objective area with the distance to the background area at each picture element, and outputs the picture data when the distance to the objective area to be extracted is smaller.

Multi-Scale Salience Distance Transforms

Abstract: The distance transform has been proposed for use in computer vision for a number of applications such as matching and skeletonisation. This paper proposes two things: (1) a multi-scale distance transform to overcome the need to choose edge thresholds and scale and (2) the addition of various saliency factors such as edge strength, length and curvature to the basic distance transform to improve its effectiveness. Results are presented for applications of matching and snake fitting.

Multifocus synthesis and its application to 3D image capturing

Abstract: A new technique for the high-resolution image synthesis called Multifocus synthesis is presented. As an impor-tant extension, the 3-D real-world image capture is discussed. In the approach, the object image is taken at a numberof focal distances by a single camera placed at a fixed position. Each of these images are then converted into the mul-tiresolution using the optimized QMP. The resultant volume of coefficients are then analyzed and 3-D distance infor-mation is computed.2. HOLOGRAPHY AND 3-D DISTANCE INFORMATIONHolography is widely accepted as the ideal means for the 3-D image presentation. However, direct capturing ofthe optical information requires the spatial resolution ofless than 1 jim, dark indoor studio, high-power laser, nomotion, expensive film and incompatibility with the conventional video camera system. Various separate approachesare being studied including the synthetic holography that uses images captured by a multitude of conventional videocameras"2.For practical implementation of the 3-D display system, computation of the 3-D distance is of fundamentalimportance. But as is known, the reconstruction of 3-D information from 2-D image alone is an ill-posed problem anda special arrangement has to be made.A large number of works have and are been made in two approaches: passive and active measurement3'4. Thepassive measurement includes the auto-focusing and the binocular parallax image capture with correspondence fea-ture matching'6. The active measurement includes the optical/radar range finders, the slit-beam projection, themoire-topography and other coded light pattern projection, which are all generally suitable for the distance measure-ment itself rather than for the object image capturing, and the measurement usually has to be made in the indoor andclosed environments. There is another approach involving the spatial-temporal image processing, for example, theanalysis of images recorded by a video camera moving in a constant speed in one direction4. This is an extension ofthe passive approach.Passive computation of the 3-D distance from two binocular parallax (stereoscopic) images has been also wellstudied in the 3-D image analysis and understandthg". Conventional techniques first identifies the correspondingfeatures between the left and right images by the optical flow or the pattern-matching of the discrete features such aspoints, lines and contours using various techniques including dynamic programming6, correlation matching and neu-ral network12. The parallax image capture and processing approach has however a fundamental difficulty concerningthe discontinuous line-of-sight at the object edges and contours due to the parallax camera positioning (occlusion).When the neural network is applied to the feature matching, the distance perception mechanism can be modelled bylayers of cooperative operators and a mutually exclusive (inhibitive) operator working on all the cooperative outputs.In the neural network solution, an incorrect distance computation tends to propagate to the neighboring cells, result-ing in a larger number of inaccurate estimates. Some of the recent studies are being made on the a priori training ofthe shapes of the 3-D objects and isolated point removal5, but as long as the binocular parallax approach is taken,there is no fundamental solution to the problem.This paper discusses a new approach to the 3-D distance computation using images captured by a single cameraplaced at a fixed position. This avoids the problem inherent with the bthocular parallax approach and uses a com-pletely different set of tools compared with the correspondence feature matching.In the following, the fundamental image processing tool called Multifocus Synthesis (MFS) is first described.MFS was originally proposed for the synthesis of the higher resolution image using several focused images'33. MTJLTIFOCUS SYNTHESISIn Optics, a perfect pin-hole is a mathematical concept of an ideal lens and everyday images captured through acamera are the result of pre-processing by the lens. Every lens has a (adjustable) focusing distance and the informa-

Grey-level encoding of openings and closings

Abstract: A distance transform will convert a bi-level image into a gray scale image, where the intensity of the object pixels is proportional to their distance from the nearest back-ground pixel This can be computed in two passes through an image, and has been used to encode all binary erosions and dilations into one `globally eroded' image It is also possible to encode all possible binary openings and closings as gray levels, allowing any particular opening or closing to be achieved through a simple thresholding operation, or by non-destructive comparisons We define nodal points in the distance transform as those which have no neighbors having the maximum possible value (For example, 7 for diagonal pixels, and 12 for others using Euclidean distance) At each of these points a digital circle can be drawn, whose values equal that of the significant point A simple histogram of the thus encoded image yields the roughness spectrum, but the spectrum found using only the significant points may be just as useful

Printed Text Segmentation Using Distance Transform

Abstract: In this paper, two new algorithms to segment printed text into words and strings using direct and reverse distance transformation are presented. It is supposed that an original image does not contain graphics. The text segmentation into words and strings is performed on the basis of different threshold values, which either are determined a priori or calculated automatically.The segmentation result does not depend on a character size and a font type. It is defined by using distances between the neighbouring strings and the neighbouring words in the same string.

Image compression using dtocs and neighborhood masks along threshold boundaries

Abstract: In this paper, a new image compression method is presented. It utilizes the DTOCS (Distance Transform on Curved Space) introduced in [Toi92) and [Toi93]. Masks of different sizes are used near threshold boundaries to select optimal places for new control points. The presented method is a considerable improvement to the method presented in [Toi93] and gives better compression ratios. Especially when the number of control points is kept low the difference is 1.5-2 dB in signal-to-noise ratio and it is visually quite clear. The decompression is done by a new method introduced in [Toi93]. It is an interpolation method based on a set of structuring elements.

On solving exact Euclidean distance transformation with invariance to object size

Abstract: A distance transformation converts a digital binary image that consists of object (foreground) and non-object (background) pixels into a gray-scale image in which each object pixel has a value corresponding to the minimum distance from the background by a distance function. Due to its nonlinearity, the global operation of Euclidean distance transformation (EDT) is difficult to decompose into small neighborhood operations. Two efficient algorithms on EDT are presented, using integers of squared Euclidean distances in which the global computations can be equivalent to local 3/spl times/3 neighborhood operations. The first algorithm requires only a limited number of iterations on the chain propagation. The second algorithm can avoid iterations, and simply requires two scans of the image. The complexity of both algorithms is only linearly proportional to image size. >

An image representation based on planar patches and the local adjustment technique

Abstract: An efficient technique for representing a grey-scale image with a collection of connected triangular planar patches is investigated The patches are planar in the three-dimensional space described by the plane of the image and using the intensity as the third dimension In this way, the image can be thought of geometrically as a surface The patches are fitted to this surface by application of the local adjustment technique >

Range from focus error

Abstract: We derive theoretically and demonstrate experimentally an approach to range-from-focus with an important improvement over all previous methods. Previous methods rely on subjective measures of sharpness to focus a selected locale of the image. Our method uses measured physical features of the optical signal to generate an objective focus-error distance map. To compute range-from-focus-error distance it is not necessary to focus any part of the image: range is calculated directly from the lens formula by substituting the difference between the lens-to-sensor distance and the focus-error distance for the usual lens-to-image distance. Our method senses focus-error distance in parallel for all locales of the image, thus providing a complete range image. The method is based on our recognition that when an image sensor is driven in longitudinal oscillation ("dithered") the Fourier amplitude of the first harmonic component of the signal is proportional to the first power of the ratio of dither amplitude to focus-error distance, whereas the Fourier amplitude of the second harmonic component is proportional to the square of this ratio. The ratio of the first harmonic sin ot amplitude A1, to the second harmonic cos 2cot amplitude B2 is thus a constant (-4) multiple of the ratio of the focus-error distance to the dither amplitude. The focus-error distance measurement via the ratio of the first-to-second harmonic amplitudes is extremely robust in the sense that the scene's gray level structure, the spatial and temporal structure of the illumination, and technical noise sources (most of which affect the Fourier amplitudes multiplicatively) all appear identically in both amplitudes, thus cancelling in the ratio. Extracting the two Fourier amplitudes and taking their ratio could be accomplished, pixel-by-pixel, by some ambitious but not outrageous analog computing circuitry that we describe. We derive the method for a point scene model, and we demonstrate the method with apparatus that instantiates this modeL

Digital distance geometry: A survey

Abstract: Digital distance geometry (ddg) is the study of distances in the geometry of digitized spaces. This was introduced approximately 25 years ago, when the study of digital geometry itself began, for providing a theoretical background to digital picture processing algorithms. In this survey we focus our attention on theddg of arbitrary dimensions and other related issues and compile an up-to-date list of references on the topic.