Medial Axis Research Articles

Average curve of [formula omitted] smooth planar curves

We define the Average Curve (AC) of a compatible set of two or more smooth and planar, Jordan curves. It is independent of their order and representation. We compare two variants: the valley AC (vAC), defined in terms of the valley of the field that sums the squared distances to the input curves, and the zero AC (zAC), defined as the zero set of the field that sums the signed distances to the input curves. Our formulation provides an orthogonal projection homeomorphism from the AC to each input curve. We use it to define compatibility. We propose a fast tracing algorithm for computing a polygonal approximation (PAC) of the AC and for testing compatibility. We provide a linear-cost implementation for tracing the PAC of polygonal approximations of smooth input curves. We also define the inflation of the AC and use it to visualize the local variability in the set of input curves. We argue that the AC and its inflation form a natural extension of the Medial Axis Transform to an arbitrary number of curves. We propose extensions to open curves and to weighted averages of curves, which can be used to design animations.

A Framework for Symmetric Part Detection in Cluttered Scenes

The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favour as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today’s recognition systems are faced with cluttered scenes and the assumption that a closed contour exists, i.e., that figure-ground segmentation has been solved, rendering much of the medial axis community’s work inapplicable. In this article, we review a computational framework, previously reported in [1–3], that bridges the representation power of the medial axis and the need to recover and group an object’s parts in a cluttered scene. Our framework is rooted in the idea that a maximally-inscribed disc, the building block of a medial axis, can be modelled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.

Enhanced medial-axis-based block-structured meshing in 2-D

New techniques are presented for using the medial axis to generate decompositions on which high quality block-structured meshes with well-placed mesh singularities can be generated. Established medial-axis-based meshing algorithms are effective for some geometries, but in general, they do not produce the most favourable decompositions, particularly when there are geometric concavities. This new approach uses both the topological and geometric information in the medial axis to establish a valid and effective arrangement of mesh singularities for any 2-D surface. It deals with concavities effectively and finds solutions that are most appropriate to the geometric shapes. Resulting meshes are shown for a number of example models.

A new method for multi-oriented graphics-scene-3D text classification in video

Text detection and recognition in video is challenging due to the presence of different types of texts, namely, graphics (video caption), scene (natural text), 2D, 3D, static and dynamic texts. Developing a universal method that works well for all the types is hard. In this paper, we propose a novel method for classifying graphics-scene and 2D–3D texts in video to enhance text detection and recognition accuracies. We first propose an iterative method to classify static and dynamic clusters based on the fact that static texts have zero velocity while dynamic texts have non-zero velocity. This results in text candidates for both static and dynamic texts regardless of 2D and 3D types. We then propose symmetry for text candidates using stroke width distances and medial axis values, which results in potential text candidates. We group potential text candidates using their geometrical properties to form text regions. Next, for each text region, we study the distribution of the dominant medial axis values given by ring radius transform in a new way to classify graphics and scene texts. Similarly, we study the proximity among the pixels that satisfy the gradient directions symmetry to classify 2D and 3D texts. We evaluate each step of the proposed method in terms of classification and recognition rates through classification with the existing methods to show that video text classification is effective and necessary for enhancing the capability of current text detection and recognition systems.

Segmentation and Localization of Optic Disc using Feature Match and Medial Axis Detection in Retinal Images

Glaucoma is an eye disease that leads to vision loss without any major symptoms. Detecting the disease in time is important because it cannot be cured. Due to raised Intra-Ocular Pressure (IOP), the Optic Nerve Head (ONH) gets damaged and the assessment of ONH is more promising because it consists of Optic Disc (OD) and Optic Cup (OC) in retinal fundus image. OD and OC detection is important preprocessing step to diagnose glaucoma. In this paper, we proposed a segmentation of OD by FeatureMatch (FM) technique and OD is localized using medial axis detection. The correspondence between the OD reference image and any input image is found by FM. This correspondence provides a distribution of patches in the input image that are closest to patches in the reference image. The proposed work is evaluated using DRIONS-DB that consists of 110 images. The OD is correctly localized in more than 60 images. The performance measures such as Root Mean Square Error (RMSE) and Mean of Structural SIMilarity (MSSIM) are calculated. The average computational time for this proposed work is about 14 secs. The average RMSE of the proposed work is about 0.05389.

A Method for Three-Dimensional Reconstruction of Apple Trees for Automated Pruning

Labor cost and availability have been a major concern for tree fruit growers, as many field operations, including tree pruning, are highly labor intensive. Currently, pruning in apple production is primarily a manual operation. However, newer orchards are being planted in simple, narrow, accessible, and productive (SNAP) architectures such as the tall spindle fruiting wall system, which provides opportunities for automated pruning. This technical note presents a method to obtain the 3D structures of apple trees and identify branches as a first step toward developing an automated pruning system. A time-of-flight-of-light-based three-dimensional (ToF 3D) camera is used to obtain 3D images of apple trees in a commercial orchard. The images are preprocessed to remove noise and fill unwanted voids. The preprocessed images are then used to generate tree skeletons using a medial axis thinning algorithm. Tree skeletons are analyzed to detect trunks and identify branches. This method successfully reconstructed 3D structures of apple trees with 100% accuracy in detecting trunks. The method achieved a branch identification accuracy of 77%, with a false negative identification of 23%. This work provides a promising method for 3D reconstruction of apple trees that can be used to generate a database of tree branches including branch length and interbranch spacing, which is critical information for developing a system for automated pruning.

Computing refined skeletal features from medial point clouds

Medial representations have been widely used for many shape analysis and processing tasks. Large and complex 3D shapes are, in this context, a challenging case. Recently, several methods have been proposed that extract point-based medial surfaces with high accuracy and computational scalability. However, the resulting medial clouds are of limited use for shape processing due to the difficulty of computing refined medial features from such clouds. In this paper, we show how to bridge the gap between having a raw medial cloud and enriching this cloud with feature points, medial-point classification, medial axis decomposition into sheets, robust regularization, and Y-network extraction. We further show how such properties can be used to support several shape processing sample applications including edge detection and shape segmentation, for a wide range of complex 3D shapes.

Fast and reliable gate arrangement pre-design of resin infusion processes

In Resin Infusion (RI) processes, the flow front shape progression is mainly conditioned by the initial arrangement of the injection and vent gate line locations and the permeability of the preform. The main goal of this research is to develop fast (not necessarily physically-based) tools at the pre-design stage that could help designers with a suitable arrangement of injection nozzles and vents. This pre-design should then be validated by full-physics simulation or lab test, but could be considered as a suitable starting point in the designing process. RI simulators could eventually be equipped with this kind of pre-design tools as a means to provide very fast (at the cost of a somewhat reduced accuracy) designs. In the approach here presented the pre-design tools are based entirely on geometrical assumptions. Under these hypotheses, and assuming that the vents will be placed on the boundary of the piece, the distance field from this boundary will provide useful information on the optimal position of injection nozzles. In this work, inspired by the concept of medial axis, we propose a numerical technique that computes numerically approximate distance fields by invoking computational geometry concepts that can be used for the estimation of the gate arrangement in infusion processes. Detailed descriptions of the developed algorithm, together with first proofs of its performance are given.

A geometry projection method for continuum-based topology optimization with discrete elements

Abstract This article describes a method for the continuum-based topology optimization of structures made of discrete elements. In particular, we examine the optimization of linearly elastic planar structures made of bars of fixed width and semicircular ends. The design space for the optimization consists of the endpoint locations of the bar’s medial axes and their out-of-plane thicknesses. To circumvent re-meshing upon design changes, we project the design onto a fixed analysis grid using a differentiable geometry projection that results in a density field indicating the fraction of solid material anywhere in the design space, as in density-based topology optimization methods. The out-of-plane thickness is penalized so that the optimizer is capable of removing bars during the optimization. The differentiability of the projection allows for the computation via the chain rule of design sensitivities of responses of interest, and therefore it allows for the use of robust and efficient gradient-based optimization methods. Notably, this approach makes it easier to fabricate optimal designs by using off-the-shelf stock material. Furthermore, the method considers the case where bars overlap at their joints (i.e. their thicknesses are added at the joint) and when they do not. Finally, our proposed method naturally accommodates the imposition of several fixed length scales. We demonstrate the proposed approach on classical problems of compliance-based topology optimization and identify its benefits as well as research directions to be addressed in the future.

Recognition of Monochrome Thermal Images of Synchronous Motor with the Application of Skeletonization and Classifier Based on Words

AbstractThermography is a technology that enables recognition of objects in the specific area. The goal of using thermographic techniques for ironworks is to diagnose electrical equipment. These techniques can be also use to increase safety and quality control in ironworks. Faulty equipment can be dangerous for engineers. Article describes the method of the recognition of imminent failure states of synchronous motor. Thermal images of the stator are used for an analysis of electrical machine. Researches of image processing techniques have been carried out for three states of motor. Proposed approach uses patterns recognition. Using of medial axis transformation and classifier based on words gave good results. In the future electrical machines and metallurgical equipment will use diagnostic systems based on recognition of thermal images.

Manufacturability Feedback and Model Correction for Additive Manufacturing

Additive manufacturing, or 3D printing, is the process of building three-dimensional solid shapes by accumulating material laid out in sectional layers. Additive manufacturing has been recognized for enabling production of complex custom parts that are difficult to manufacture otherwise. However, the dependence on build orientation and physical limitations of printing processes invariably lead to geometric deviations between manufactured and designed shapes that are usually evaluated after manufacture. In this paper, we formalize the measurement of such deviations in terms of a printability map that simulates the printing process and partitions each printed layer into disjoint regions with distinct local measures of size. We show that manufacturing capabilities, such as printing resolution, and material specific design recommendations, such as minimal feature sizes, may be coupled in the printability map to evaluate expected deviations before manufacture. Furthermore, we demonstrate how partitions with size measures below required resolutions may be modified using properties of the medial axis transform and use the corrected printability map to construct a representation of the manufactured model. We conclude by discussing several applications of the printability map for additive manufacturing.

Calculating the medial axis of a CAD model by multi-CPU based parallel computation

Computational efficiency is still a great challenge for the generation of the Medial Axis (MA) for complicated CAD models. Current research mainly focuses on CPU-based MA generation methods. However, most of the methods emphasize using a single CPU. The highly-efficient methods based on parallel computing are still missing. In this study, a parallel method based on multi-CPU is proposed for the efficient MA generation of CAD models using distance dilation. By dividing the whole model into several parts for which MAs are calculated in parallel and then combined, computational efficiency can be greatly improved in theory and the computation time can be reduced nearly K times if K CPUs are used. Firstly, an adaptive division method is proposed to divide the voxelized model into blocks which have nearly the same number of voxels to balance the computational burden. Secondly, the local Euclidean Distance Transform (EDT) is calculated for each block based on the existing distance dilation method. Thirdly, the complete inter-dilation method is proposed to compute the influence between different blocks to get a global EDT for each block. Finally, each block generates a sub-MA separately and then all the generated MAs are combined to obtain the final MA. The last three processes can be efficiently conducted in parallel by using multiple CPUs. Several groups of experiments are conducted which demonstrate the good performance of the proposed methods in terms of efficiency.

Medial axis tree—an internal supporting structure for 3D printing

Saving material and improving strength are two important but conflicting requirements in 3D printing. We propose a novel method for designing the internal supporting frame structures of 3D objects based on their medial axis such that the objects are fabricated with minimal amount of material but can still withstand specified external load. Our method is inspired by the observation that the medial axis, being the skeleton of an object, serves as a natural backbone structure of the object to improve its resistance to external loads. A hexagon-dominant framework beneath the boundary surface is constructed and a set of tree-like branching bars are designed to connect this framework to the medial axis. The internal supporting structure is further optimized to minimize the material cost subject to strength constraints. Models fabricated with our method are intended to withstand external loads from various directions, other than just from a particular direction as considered in some other existing methods. Experimental results show that our method is capable of processing various kinds of input models and producing stronger and lighter 3D printed objects than those produced with other existing methods.

Canal surfaces with rational contour curves and blends bypassing the obstacles

In this paper, we will present an algebraic condition, see (20), which guarantees that a canal surface, given by its rational medial axis transform (MAT), possesses rational generalized contours (i.e., contour curves with respect to a given viewpoint). The remaining computational problem of this approach is how to find the right viewpoint. The canal surfaces fulfilling this distinguished property are suitable for being taken as modeling primitives when some rational approximations of canal surfaces are required. Mainly, we will focus on the low-degree cases such as quadratic and cubic MATs that are especially useful for applications. To document a practical usefulness of the presented approach, we designed and implemented two simple algorithms for computing rational offset blends between two canal surfaces based on the contour method which do not need any further advanced formalism (as e.g. interpolations with MPH curves). A main advantage of the designed blending technique is its simplicity and also an adaptivity to choose a suitable blend satisfying certain constrains (avoiding obstacles, bypassing other objects, etc.). Compared to other similar methods, our approach requires only one SOS decomposition for the whole family of rational canal surfaces sharing the same silhouette, which significantly simplifies the computational complexity.

A Bayesian Approach to Perceptual 3D Object-Part Decomposition Using Skeleton-Based Representations

We present a probabilistic approach to shape decomposition that creates a skeleton-based shape representation of a 3D object while simultaneously decomposing it into constituent parts. Our approach probabilistically combines two prominent threads from the shape literature: skeleton-based (medial axis) representations of shape, and part-based representations of shape, in which shapes are combinations of primitive parts. Our approach recasts skeleton-based shape representation as a mixture estimation problem, allowing us to apply probabilistic estimation techniques to the problem of 3D shape decomposition, extending earlier work on the 2D case. The estimated 3D shape decompositions approximate human shape decomposition judgments. We present a tractable implementation of the framework, which begins by over-segmenting objects at concavities, and then probabilistically merges them to create a distribution over possible decompositions. This results in a hierarchy of decompositions at different structural scales, again closely matching known properties of human shape representation. The probabilistic estimation procedures that arise naturally in the model allow effective prediction of missing parts. We present results on shapes from a standard database illustrating the effectiveness of the approach.

Character shape restoration system through medial axis points in video

Shape restoration for characters in video is challenging because natural scene characters usually suffer from low resolution, complex background and perspective distortion. In this paper, we propose histogram gradient division and reverse gradient orientation in a new way to select Text Pixel Candidates (TPC) for a given input character. We apply a ring radius transform on TPC in different directions, namely, horizontal, vertical, principal and secondary diagonals in a TPC image to obtain respective radius maps, where each pixel is assigned a value that is the radius to the nearest TPC. This helps in finding Medial Axis Points (MAP) by searching for the maximum radius values from their neighborhoods in a radius image. The union of all the medial axis points obtained from the respective directions at each location is considered as Candidate Medial Axis Points (CMAP) of the character. Then color difference and k-means clustering are proposed to eliminate false CMAP, which outputs Potential Medial Axis Points (PMAP). We finally propose a novel way to restore the shape of the character from the PMAP. The method is tested on a video dataset and the benchmark ICDAR 2013 dataset to show its effectiveness for complex background and low resolution. Experimental results show that the proposed method is superior to the existing methods in terms of shape restoration error and recognition rate.

A medial‐axis‐based model for propagating cracks in a regularised bulk

SummaryA new continuous‐discontinuous strategy for the simulation of failure is presented. The continuous bulk is regularised by means of a gradient‐enhanced damage model, where non‐locality is introduced at the level of displacements. As soon as the damage parameter is close or equal to 1, a traction‐free crack is introduced. To determine the direction of crack growth, a new criterion is proposed. In contrast to traditional techniques, where mechanical criteria are used to define the crack path, here, a geometrical approach is used. More specifically, given a regularised damage field D(x), we propose to propagate the discontinuity following the direction dictated by the medial axis of the isoline (or isosurface in 3D) D(x) = D*. The proposed approach is tested on different two‐dimensional and three‐dimensional examples that illustrate that this combined methodology is able to deal with damage growth and material separation. Copyright © 2014 John Wiley & Sons, Ltd.

The Ellipsoid Factor for Quantification of Rods, Plates, and Intermediate Forms in 3D Geometries.

The ellipsoid factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid that fits inside the structure and that contains the point of interest, and ranges from −1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prolate (javelin-shaped) ellipsoids. For an ellipsoid with axes a ≤ b ≤ c, EF = a/b − b/c. Here, EF is demonstrated in a Java plugin, “Ellipsoid Factor” for ImageJ, distributed in the BoneJ plugin collection. Ellipsoid Factor utilizes an ellipsoid optimization algorithm, which assumes that maximal ellipsoids are centered on the medial axis, then dilates, rotates, and translates slightly each ellipsoid until it cannot increase in volume any further. EF successfully identifies rods, plates, and intermediate structures within trabecular bone, and summarizes the distribution of geometries with an overall EF mean and SD, EF histogram, and Flinn diagram displaying a/b versus b/c. EF is released to the community for testing, use, and improvement.

A practical path planning methodology for wire and arc additive manufacturing of thin-walled structures

This paper presents a novel methodology to generate deposition paths for wire and arc additive manufacturing (WAAM). The medial axis transformation (MAT), which represents the skeleton of a given geometry, is firstly extracted to understand the geometry. Then a deposition path that is based on the MAT is efficiently generated. The resulting MAT-based path is able to entirely fill any given cross-sectional geometry without gaps. With the variation of step-over distance, material efficiency alters accordingly for both solid and thin-walled structures. It is found that thin-walled structures are more sensitive to step-over distance in terms of material efficiency. The optimal step-over distance corresponding to the maximum material efficiency can be achieved for various geometries, allowing the optimization of the deposition parameters. Five case studies of complex models including solid and thin-walled structures are used to test the developed methodology. Experimental comparison between the proposed MAT-based path patterns and the traditional contour path patterns demonstrate significant improved performance in terms of gap-free cross-sections. The proposed path planning strategy is shown to be particularly beneficial for WAAM of thin-walled structures. A novel path planning methodology based on the Medial Axis Transformation (MAT) of the geometry is proposed.Gap-free paths can be obtained for any arbitrarily shaped geometry.Relationships between step-over distance and material efficiency are analysed.Optimal step-over distances for different Additive Manufacturing (AM) systems are discussed.The proposed path planning strategy is particularly useful for wire and arc additive manufacturing of thin-walled structures.

A new ring radius transform-based thinning method for multi-oriented video characters

Thinning that preserves visual topology of characters in video is challenging in the field of document analysis and video text analysis due to low resolution and complex background. This paper proposes to explore ring radius transform (RRT) to generate a radius map from Canny edges of each input image to obtain its medial axis. A radius value contained in the radius map here is the nearest distance to the edge pixels on contours. For the radius map, the method proposes a novel idea for identifying medial axis (middle pixels between two strokes) for arbitrary orientations of the character. Iterative-maximal-growing is then proposed to connect missing medial axis pixels at junctions and intersections. Next, we perform histogram on color information of medial axes with clustering to eliminate false medial axis segments. The method finally restores the shape of the character through radius values of medial axis pixels for the purpose of recognition with the Google Open source OCR (Tesseract). The method has been tested on video, natural scene and handwritten characters from ICDAR 2013, SVT, arbitrary-oriented data from MSRA-TD500, multi-script character data and MPEG7 object data to evaluate its performances at thinning level as well as recognition level. Experimental results comparing with the state-of-the-art methods show that the proposed method is generic and outperforms the existing methods in terms of obtaining skeleton, preserving visual topology and recognition rate. The method is also robust to handle characters of arbitrary orientations.