Efficient Euclidean distance transform using perpendicular bisector segmentation

A fast and exact Euclidean distance transformation using decomposed grayscale morphological operators is presented. Applied on a binary image, a distance transformation assigns each object pixel a value that corresponds to the shortest distance between the object pixel and the background pixels. It is shown that the large structuring element required for the Euclidean distance transformation can be easily decomposed into 3/spl times/3 windows. This is possible because the square of the Euclidean distance matrix changes uniformly both in the vertical and horizontal directions. A simple extension for a 3D Euclidean distance transformation is discussed. A fast distance transform for serial computers is also presented. Acting like thinning algorithms, the version for serial computers focuses operations only on the potential changing pixels and propagates from the boundary of objects, significantly reducing execution time. Nonsquare pixels can also be used in this algorithm. An example application, shape filtering using arbitrary sized circular dilation and erosion, is discussed. Rotation-invariant basic morphological operations can be done using this example application. >

In this article, we present the Euclidean distance transformation (EDT) of three-dimensional (3D) binary pictures and applications, with stress on Dr. Toyofumi Saito's work in collaboration with one of the authors. First, EDT, skeletons, and reverse EDT are defined, and then the algorithms to perform them are presented. Next, a sequential-type 3D thinning algorithm that preserves the topology of an input object is introduced. This algorithm is derived by combining an ordinary two-dimensional thinning algorithm with EDT. Finally, applications to medical image processing are presented such as automated path finding in virtual endoscopy, as well as analysis of 3D pathological sample images. Dr. Toyofumi Saito, an associate professor who was one of the most active researchers in the field of image processing in Japan and a young leader of the author's laboratory, and who was initially scheduled to be the first author of this paper, passed away on 26 October 2000. We have lost a most reliable and most promising colleague, an experienced supervisor, and a very sincere friend. He is deeply missed by all in his family, his friends, and his colleagues. On behalf of the laboratory the authors wish to dedicate this short note in memory of Dr. Toyofumi Saito and to express our sincere condolences to his loved ones.

A distance transformation (DT) takes a binary image as input and generates a distance map image in which the value of each pixel is its distance to a given set of object pixels in the binary image. In this research, DT's for multi class data (MCDTs) are developed which generate both a distance map and a class map containing for each pixel the class of the closest object. Results indicate that the MCDT based on the Fast Exact Euclidean Distance (FEED) method is a factor 2 tot 4 faster than MCDTs based on exact or semi-exact euclidean distance (ED) transformations, and is only a factor 2 to 4 slower than the MCDT based on the crude city-block approximation of the ED. In the second part of this research, the MCDTs were adapted such that they could be used for the fast generation of distance and class maps for video sequences. The frames of the sequences contain a number of fixed objects and a moving object, where each object has a separate label. Results show that the FEED based version is a factor 2 to 3.5 faster than the fastest of all the other video-MCDTs which is based on the chamfer 3,4 distance measure. FEED is even a factor 3.5 to 10 faster than another fast exact ED transformation. With video, multi class FEED it will be possible to measure distances from a moving object to various identified stationary objects with nearly the frame rate of a webcam. This will be very useful when the risk exists that objects move outside surveillance limits.

Medial Axis (MA), also known as Centres of Maximal Disks, is a useful representation of a shape for image description and analysis. MA can be computed on a distance transform, where each point is labelled to its distance to the background. Recent algorithms allow to compute Squared Euclidean Distance Transform (SEDT) in linear time in any dimension. While these algorithms provide exact measures, the only known method to characterize MA on SEDT, using local tests and Look-Up Tables, is limited to 2D and small distance values [5]. We have proposed in [14] an algorithm which computes the look-up table and the neighbourhood to be tested in the case of chamfer distances. In this paper, we adapt our algorithm for SEDT in arbitrary dimension and show that results have completely different properties.

This paper proposes a new recognition approach for traffic light based on Euclidean distance transform (EDT) and local contour pattern (LCP). There are two main contributions of this paper. First, this paper combines principle component analysis (PCA) with EDT-based image to detect traffic light colors. The color space for specific colors is partitioned more precisely, which leads to a high recognition rate. Second, we incorporate the above color detection into the contour segmentation of traffic light holder based on the LCP to further improve the recognition rate of traffic light. The experimental results show that our approach is able to detect traffic light far away from camera about 50–80 m and the average recognition rate can reach up to 99.29 %.

The cortical thickness has been used as a biomarker to assess different cerebral conditions and to detect alterations in the cortical mantle. In this work, we compare methods from the FreeSurfer software, the Computational Anatomy Toolbox (CAT12), a Laplacian approach and a new method here proposed, based on the Euclidean Distance Transform (EDT), and its corresponding computational phantom designed to validate the calculation algorithm. At region of interest (ROI) level, within- and inter-method comparisons were carried out with a test-retest analysis, in a subset comprising 21 healthy subjects taken from the Multi-Modal MRI Reproducibility Resource (MMRR) dataset. From the Minimal Interval Resonance Imaging in Alzheimer's Disease (MIRIAD) data, classification methods were compared in their performance to detect cortical thickness differences between 23 healthy controls (HC) and 45 subjects with Alzheimer's disease (AD). The validation of the proposed EDT-based method showed a more accurate and precise distance measurement as voxel resolution increased. For the within-method comparisons, mean test-retest measures (percentages differences/intraclass correlation/Pearson correlation) were similar for FreeSurfer (1.80%/0.90/0.95), CAT12 (1.91%/0.83/0.91), Laplacian (1.27%/0.89/0.95) and EDT (2.20%/0.88/0.94). Inter-method correlations showed moderate to strong values (R > 0.77) and, in the AD comparison study, all methods were able to detect cortical alterations between groups. Surface- and voxel-based methods have advantages and drawbacks regarding computational demands and measurement precision, while thickness definition was mainly associated to the cortical thickness absolute differences among methods. However, for each method, measurements were reliable, followed similar trends along the cortex and allowed detection of cortical atrophies between HC and patients with AD.

Euclidean distance transformation (EDT) is used to convert a digital binary image consisting of object (foreground) and nonobject (background) pixels into another image where each pixel has a value of the minimum Euclidean distance from nonobject pixels. In this paper, the improved iterative erosion algorithm is proposed to avoid the redundant calculations in the iterative erosion algorithm. Furthermore, to avoid the iterative operations, the two-scan-based algorithm by a deriving approach is developed for achieving EDT correctly and efficiently in a constant time. Besides, we discover when obstacles appear in the image, many algorithms cannot achieve the correct EDT except our two-scan-based algorithm. Moreover, the two-scan-based algorithm does not require the additional cost of preprocessing or relative-coordinates recording.

Prediction method of dust pollutant diffusion range in building demolition based on Euclidean distance transformation

In this paper, we examine the use of implicit shape representations for nonrigid registration of serial CT liver examinations. Using ground truth in the form of corresponding landmarks manually labeled by a radiotherapist, we carry out an experiment to determine whether nonrigid registration performs better when applied to the original image data or to images constructed from implicit representations of the liver. We compare a variety of standard regularizers (elastic, diffusion, and curvature), similarity measures (sum of squared differences and mutual information), and weighting factors, using three different implicit shape representations: the Euclidean Distance Transform, the Poisson Transform (based on the expected hitting time of a random walk), and a new transform designed to highlight concavities in the shape.

The Euclidean distance transform in arbitrary dimensions

Fast erosion and dilation by contour processing and thresholding of distance maps

A contour to grid conversion method is proposed. In the proposed method, Euclidean distance transformation is used to determine the nearest points on the contour with which given point is to be interpolated. By using this approach, complicated searching process of standard points for interpolation could be avoided, which results in simplified and stabilized algorithm. Also, the method can be applied to the contours which are not completely closed. Hence, the burden for restoration of contour can be reduced.The conversion accuracy is evaluated by comparing the result with human-interpreted grid data. An average error for closed contours is 37cm when the elevation interval for contour is 10m, which is thought to be acceptable for many applications. Even in the case of not completely closed contours, the average error is 38cm, which is negligible degradation of accuracy compared to completely closed case.

In this work, a fast shape searching face alignment (F-SSFA) algorithm based accelerator is proposed to achieve real-time processing. Firstly, a learning based low-dimensional SURF feature is introduced to reduce the computation cost in the cascaded regression. Then the Euclidean distance and shape affine transformation are utilized to accelerate the shape searching procedure. F-SSFA therefore greatly reduces the computational complexity while keeping the same accuracy. Also, a fixed-point F-SSFA based VLSI architecture is designed with approximately 80% decrease in the data transmission traffic. The throughput of this accelerator achieves 700 fps, which is especially suitable for high-speed facial-related applications.

Most of the welding robots in practice are still teaching and playback mode. They are lack of the function to perceive the external environment, so it is difficult to carry out adaptive welding pass arrangement and position planning for medium thick plate. In this research, extraction procedure for feature points in laser stripe is presented. We get the weld groove profile with laser scanning. After processing the laser stripe with some image process methods, we get the two lowest feature points of the laser stripe including binarize image, medium filter for image, extracting the center of laser stripe. Then, two target feature points are extracted with linear fitting and distance formula. Finally, we convert the image coordinate value to the TCP coordinate of the robot according to the calibration matrixes. As a result, we restored the physical cross section of the weld bead, and can decide the initial welding position with the two feature points for every welding pass in the medium thick plates.

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.