Computing 3D Medial Axis for Chamfer Distances

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.

Deep learning-based automated detection of the dental crown finish line: An accuracy study

This paper describes a number of efficient algorithms for morphological operations which use discs defined by chamfer distances as structuring elements. It presents an extension to previous work on extending metrics (such as the p-q-metrics). Theoretical results and algorithms are presented for p-q-r-metrics, which are not extending. These metrics can approximate the Euclidean metric close enough for most practical situations. The algorithms are based on an analysis of the structure of shortest paths in the p-q-r-metric and of the set of values this metric can assume. Efficient algorithms are presented for the medial axis and the opening transform. The opening transform algorithm is two orders of magnitude faster than a more straightforward algorithm.

Chapter 19 - The Medial Axis Transform

We propose a novel learning algorithm, called Bagging-Adaboost ensemble algorithm with genetic algorithm post optimization, for object detection that uses local shape-based feature. The feature is motivated by the scheme that use the chamfer distance as a shape comparison measure. It can be calculated very quickly using a look-up table. Random sampling boosting algorithm is used to select a discriminative edge shape features set from a over-complete dictionary of features and form an object detector. Genetic Algorithm post optimization procedure is used to remove based classifiers which cause higher error rates. The resulting classifier consists of fewer base classifiers yet achieves better generalization performance. To demonstrate our method we trained a system to detect pedestrians in complex natural scenes. Experimental results show that our system can extremely rapidly detect objects with high detection rate. The result is very competitive with other published object detection schemes. The learning techniques can be extended to detect other objects.

Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon "small" neighborhoods still outperforms it e.g. in terms of computation time. In this paper we determine the best possible maximum relative error of chamfer distances under various boundary conditions. In each case some best approximating sequences are explicitly given. Further, because of possible practical interest, we give all best approximating sequences in case of small (i.e. 5x5 and 7x7) neighborhoods.

CAD models serve as the fundamental carriers for representing geometric structures and design logic. Understanding the underlying construction logic of complex shapes facilitates the reuse, editing, and optimization of designs. Constructive Solid Geometry (CSG) offers a viable approach for shape parsing by representing complex geometries through combinations of simple primitives. This paper proposes a novel method for parsing 3D CAD shapes based on CSG representations. Leveraging quadric surfaces as the fundamental modeling primitives, our approach employs a dual-branch architecture— “composition–subtraction”—to construct target 3D shapes via Boolean operations. Each branch receives either voxel grids or point clouds as input and uses an auto-encoder to extract shape features, which are then used to predict a set of intermediate shapes. The final reconstruction is obtained through set difference operations. To enhance the model’s expressive capacity under a fixed Boolean operation sequence, we introduce rotation parameters and dual primitive designs. Moreover, we adopt a staged training framework that progressively guides the model from learning approximate signed distance functions to precise structural modeling. A regularization loss is incorporated to promote geometric diversity and plausibility of the primitives. After training, we further propose a post-processing strategy based on signed distance influence to remove redundant primitives, resulting in more compact and interpretable CSG sequences. Experimental comparisons on the ABC dataset demonstrate that our method reduces the 3D chamfer distance and edge chamfer distance by 72.1% and 31.1%, respectively, and improves the normal vector consistency by 9.48%, compared to SECAD-Net, and achieves better results in visual metrics.

The mutagenic effect of chemicals is assessed using a procedure which examines their effect on the shapes of chromosomes in cells. Even slight changes in chromosome configurations can adversely affect an organism as a whole. The identification of damage in cells is time consuming. Automating the identification would considerably reduce the procedure time. This paper gives a new way of characterizing damaged chromosomes and distinguishing them from normal chromosomes. The methodology builds on previous work which is relevant, but not directly related to the problem.The approach is based on the fact that all normal chromosomes have a characteristic X shape, which can be described by their medial axis. The most common chemical mutation structures, exchange figures, do not exhibit this characteristic. Using the medial axis in conjunction with other features, it is possible to classify a chromosome as normal or abnormal.KeywordsMedial AxisExchange FigureNormal ChromosomeDamage ChromosomeDicentric ChromosomeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric representations, despite increased popularity of 3D surface and shape data in medical image analysis. We propose a one-step registration model for 3D surfaces that internalises a lower dimensional probabilistic deformation model (PDM) using conditional variational autoencoders (CVAE). The deformations are constrained to be diffeomorphic using an exponentiation layer. The one-step registration model is benchmarked against iterative techniques, trading in a slightly lower performance in terms of shape fit for a higher compactness. We experiment with two distance metrics, Chamfer distance (CD) and Sinkhorn divergence (SD), as specific distance functions for surface data in real-world registration scenarios. The internalised deformation model is benchmarked against linear principal component analysis (PCA) achieving competitive results and improved generalisability from lower dimensions.

BackgroundMany human muscle wasting diseases are associated with abnormal nuclear localization. During metamorphosis in Drosophila melanogaster, multi-nucleated larval dorsal abdominal muscles either undergo cell death or are remodeled to temporary adult muscles. Muscle remodeling is associated with anti-polar nuclear migration and atrophy during early pupation followed by polar migration and muscle growth during late pupation. Muscle remodeling is a useful model to study genes involved in myonuclear migration. Previously, we showed that loss of Cathepsin-L inhibited anti-polar movements, while knockdown of autophagy-related genes affected nuclear positioning along the medial axis in late metamorphosis.ResultsTo compare the phenotypic effects of gene perturbations on nuclear migration more objectively, we developed new descriptors of myonuclear distribution. To obtain nuclear pattern features, we designed an algorithm to detect and track nuclear regions inside live muscles. Nuclear tracks were used to distinguish between fast moving nuclei associated with fragments of dead muscles (sarcolytes) and slow-moving nuclei inside remodelled muscles. Nuclear spatial pattern features, such as longitudinal (lonNS) and lateral nuclear spread (latNS), allowed us to compare nuclear migration during muscle remodelling in different genetic backgrounds. Anti-polar migration leads to a lonNS decrease. As expected, lack of myonuclear migration caused by the loss of Cp1 was correlated with a significantly lower lonNS decrease. Unexpectedly, the decrease in lonNS was significantly enhanced by Atg9, Atg5 and Atg18 silencing, indicating that the loss of autophagy promotes the migration and clustering of nuclei. Loss of autophagy also caused a scattering of nuclei along the lateral axis, leading to a two-row as opposed to single row distribution in control muscles. Increased latNS resulting from knockdown of Atg9 and Atg18 was correlated with increased muscle diameter, suggesting that the wider muscle fibre promotes lateral displacement of nuclei from the medial axis during polar migration.ConclusionsWe developed new nuclear features to characterize the dynamics of nuclear distribution in time-lapse images of Drosophila metamorphosis. Image quantification improved our understanding of phenotypic abnormalities in nuclear distribution resulting from gene perturbations. Therefore, in vivo imaging and quantitative image analysis of Drosophila metamorphosis promise to provide novel insights into the relationship between muscle wasting and myonuclear positioning.

A fusion-based approach for uterine cervical cancer histology image classification

This paper is devoted to the study of the medial axes of sets definable in polynomially bounded o-minimal structures, i.e. the sets of points with more than one closest point with respect to the Euclidean distance. Our point of view is that of singularity theory. While trying to make the paper self-contained, we gather here also a large bunch of basic results. Our main interest, however, goes to the characterization of those singular points of a definable, closed set Xsubset {mathbb {R}}^n, which are reached by the medial axis.

Point cloud registration is a central theme in computer vision, with alignment algorithms continuously improving for greater robustness. Commonly used methods evaluate Euclidean distances between point clouds and minimize an objective function, such as Root Mean Square Error (RMSE). However, these approaches are most effective when the point clouds are well-prealigned and issues such as differences in density, noise, holes, and limited overlap can compromise the results. Traditional methods, such as Iterative Closest Point (ICP), require choosing one point cloud as fixed, since Euclidean distances lack commutativity. When only one point cloud has issues, adjustments can be made, but in real scenarios, both point clouds may be affected, often necessitating preprocessing. The authors introduce a novel differential entropy-based metric, designed to serve as the objective function within an optimization framework for fine rigid pairwise 3D point cloud registration, denoted as Iterative Differential Entropy Minimization (IDEM). This metric does not depend on the choice of a fixed point cloud and, during transformations, reveals a clear minimum corresponding to the best alignment. Multiple case studies are conducted, and the results are compared with those obtained using RMSE, Chamfer distance, and Hausdorff distance. The proposed metric proves effective even with density differences, noise, holes, and partial overlap, where RMSE does not always yield optimal alignment.

Artificial Intelligence in the American Healthcare Industry: Looking Forward to 2030

The main steps of image analysis are image capturing, image storage (compression), correcting imaging defects (e.g. non-uniform illumination, electronic-noise, glare effect), image enhancement, segmentation of objects in the image and image measurements. Digitisation is made by a camera. The most modern types include a frame-grabber, converting the analog-to-digital signal into digital (numerical) information. The numerical information consists of the grey values describing the brightness of every point within the image, named a pixel. The information is stored in bits. Eight bits are summarised in one byte. Therefore, grey values can have a value between 0 and 256 (2(8)). The human eye seems to be quite content with a display of 5-bit images (corresponding to 64 different grey values). In a digitised image, the pixel grey values can vary within regions that are uniform in the original scene: the image is noisy. The noise is mainly manifested in the background of the image. For an optimal discrimination between different objects or features in an image, uniformity of illumination in the whole image is required. These defects can be minimised by shading correction [subtraction of a background (white) image from the original image, pixel per pixel, or division of the original image by the background image]. The brightness of an image represented by its grey values can be analysed for every single pixel or for a group of pixels. The most frequently used pixel-based image descriptors are optical density, integrated optical density, the histogram of the grey values, mean grey value and entropy. The distribution of the grey values existing within an image is one of the most important characteristics of the image. However, the histogram gives no information about the texture of the image. The simplest way to improve the contrast of an image is to expand the brightness scale by spreading the histogram out to the full available range. Rules for transforming the grey value histogram of an existing image (input image) into a new grey value histogram (output image) are most quickly handled by a look-up table (LUT). The histogram of an image can be influenced by gain, offset and gamma of the camera. Gain defines the voltage range, offset defines the reference voltage and gamma the slope of the regression line between the light intensity and the voltage of the camera. A very important descriptor of neighbourhood relations in an image is the co-occurrence matrix. The distance between the pixels (original pixel and its neighbouring pixel) can influence the various parameters calculated from the co-occurrence matrix. The main goals of image enhancement are elimination of surface roughness in an image (smoothing), correction of defects (e.g. noise), extraction of edges, identification of points, strengthening texture elements and improving contrast. In enhancement, two types of operations can be distinguished: pixel-based (point operations) and neighbourhood-based (matrix operations). The most important pixel-based operations are linear stretching of grey values, application of pre-stored LUTs and histogram equalisation. The neighbourhood-based operations work with so-called filters. These are organising elements with an original or initial point in their centre. Filters can be used to accentuate or to suppress specific structures within the image. Filters can work either in the spatial or in the frequency domain. The method used for analysing alterations of grey value intensities in the frequency domain is the Hartley transform. Filter operations in the spatial domain can be based on averaging or ranking the grey values occurring in the organising element. The most important filters, which are usually applied, are the Gaussian filter and the Laplace filter (both averaging filters), and the median filter, the top hat filter and the range operator (all ranking filters). Segmentation of objects is traditionally based on threshold grey values. (AB