Minima Rule Research Articles

Models partition for 3D printing objects using skeleton

PurposeIt is a challenge to print a model with the size that is larger than the working volume of a three-dimensional (3D) printer. The purpose of this paper is to present a feasible approach to divide a large model into small printing parts to fit the volume of a printer and then assemble these parts into the final model.Design/methodology/approachThe proposed approach is based on the skeletonization and the minima rule. The skeleton of a printing model is first extracted using the mesh contraction and the principal component analysis. The 3D model is then partitioned preliminarily into many smaller parts using the space sweep method and the minima rule. The preliminary partition is finally optimized using the greedy algorithm.FindingsThe skeleton of a 3D model can effectively represent a simplified version of the geometry of the 3D model. Using a model’s skeleton to partition the model is an efficient way. As it is generally desirable to have segmentations at concave creases and seams, the cutting position should be located in the concave region. The proposed approach can partition large models effectively to well retain the integrity of meaningful parts.Originality/valueThe proposed approach is new in the rapid prototyping field using the model skeletonization and the minima rule. Based on the authors’ knowledge, there is no method that concerns the integrity of meaningful parts for partitioning. The proposed method can achieve satisfactory results by the integrity of meaningful parts and assemblability for most 3D models.

An Improved Approach of Mesh Segmentation to Extract Feature Regions.

The objective of this paper is to extract concave and convex feature regions via segmenting surface mesh of a mechanical part whose surface geometry exhibits drastic variations and concave-convex features are equally important when modeling. Referring to the original approach based on the minima rule (MR) in cognitive science, we have created a revised minima rule (RMR) and presented an improved approach based on RMR in the paper. Using the logarithmic function in terms of the minimum curvatures that are normalized by the expectation and the standard deviation on the vertices of the mesh, we determined the solution formulas for the feature vertices according to RMR. Because only a small range of the threshold parameters was selected from in the determined formulas, an iterative process was implemented to realize the automatic selection of thresholds. Finally according to the obtained feature vertices, the feature edges and facets were obtained by growing neighbors. The improved approach overcomes the inherent inadequacies of the original approach for our objective in the paper, realizes full automation without setting parameters, and obtains better results compared with the latest conventional approaches. We demonstrated the feasibility and superiority of our approach by performing certain experimental comparisons.

Segmentation of 3D Meshes Using p-Spectral Clustering.

In this paper, we propose a new approach to get the optimal segmentation of a 3D mesh as a human can perceive using the minima rule and spectral clustering. This method is fully unsupervised and provides a hierarchical segmentation via recursive cuts. We introduce a new concept of the adjacency matrix based on cognitive studies. We also introduce the use of one-spectral clustering which leads to the optimal Cheeger cut value.

The bag of words approach for retrieval and categorization of 3D objects

In this paper, we propose a novel framework for 3D object retrieval and categorization. The object is modeled in terms of its subparts as an histogram of 3D visual word occurrences. We introduce an effective method for hierarchical 3D object segmentation driven by the minima rule that combines spectral clustering—for the selection of seed-regions—with region growing based on fast marching. Descriptors attached to the regions allow the definition of the visual words. After coding of each object according to the Bag-of-Words paradigm, retrieval can be performed by matching with a suitable kernel, or categorization by learning a Support Vector Machine. Several examples on the Aim@Shape watertight dataset and on the Tosca dataset demonstrate the versatility of the proposed method in working with either 3D objects with articulated shape changes or partially occluded or compound objects. Results are encouraging as shown by the comparison with other methods for each of the analyzed scenarios.

A Part‐aware Surface Metric for Shape Analysis

AbstractThe notion of parts in a shape plays an important role in many geometry problems, including segmentation, correspondence, recognition, editing, and animation. As the fundamental geometric representation of 3D objects in computer graphics is surface‐based, solutions of many such problems utilize a surface metric, a distance function defined over pairs of points on the surface, to assist shape analysis and understanding. The main contribution of our work is to bring together these two fundamental concepts: shape parts and surface metric. Specifically, we develop a surface metric that is part‐aware. To encode part information at a point on a shape, we model its volumetric context – called the volumetric shape image (VSI) – inside the shape's enclosed volume, to capture relevant visibility information. We then define the part‐aware metric by combining an appropriate VSI distance with geodesic distance and normal variation. We show how the volumetric view on part separation addresses certain limitations of the surface view, which relies on concavity measures over a surface as implied by the well‐known minima rule. We demonstrate how the new metric can be effectively utilized in various applications including mesh segmentation, shape registration, part‐aware sampling and shape retrieval.

Visual Salience-Guided Mesh Decomposition

In this paper, we propose a novel mesh-decomposition scheme called salience-guided mesh decomposition. The concept of salience, which originated in cognitive psychology, asserts that the salience of a part can be determined by (at least) three factors: the protrusion, the boundary strength, and the relative size of the part. We try to convert these conceptual rules into real computational processes, and use them to guide a three-dimensional (3D) mesh decomposition process in such a way that the significant components can be precisely identified and efficiently extracted from a given 3D mesh. The proposed decomposition scheme not only identifies the parts' boundaries defined by the minima rule, but also labels each part with a quantitative degree of visual salience during the mesh decomposition process. The experimental results show that the proposed scheme is indeed effective and powerful in decomposing a 3D mesh into its significant components

Mesh scissoring with minima rule and part salience

This paper presents an intelligent scissoring operator for meshes. Unlike common approaches that segment a mesh using clustering schemes, here we introduce a method that concentrates on the contours for cutting. Our approach is based on the minima rule and part salience theory from the cognitive theory. The minima rule states that human perception usually divides a surface into parts along the concave discontinuity of the tangent plane. The part salience theory provides factors which determine the salience of segments. Our method first extracts features to find candidate contours based on the minima rule. Subsequently, these open contours are prioritized to select the most salient one. Then, the selected open contour is automatically completed to form a loop around a specific part of the mesh. This loop is used as the initial position of a 3D geometric snake. Before applying a snake, we measure the part salience of the segments obtained by the completed contour. If conditions for the salience are not met, the contour is rejected. Otherwise, the snake moves by relaxation until it settles to define the final scissoring position. In this paper, we focus on a fully automatic scissoring scheme; nevertheless, we also report on semi-automatic user interfaces for intelligent scissoring which are easy to use and intuitive.

Parts of visual objects: an experimental test of the minima rule.

Three experiments were conducted to test Hoffman and Richards's (1984) hypothesis that, for purposes of visual recognition, the human visual system divides three-dimensional shapes into parts at negative minima of curvature. In the first two experiments, subjects observed a simulated object (surface of revolution) rotating about a vertical axis, followed by a display of four alternative parts. They were asked to select a part that was from the object. Two of the four parts were divided at negative minima of curvature and two at positive maxima. When both a minima part and a maxima part from the object were presented on each trial (experiment 1), most of the correct responses were minima parts (101 versus 55). When only one part from the object--either a minima part or a maxima part--was shown on each trial (experiment 2), accuracy on trials with correct minima parts and correct maxima parts did not differ significantly. However, some subjects indicated that they reversed figure and ground, thereby changing maxima parts into minima parts. In experiment 3, subjects marked apparent part boundaries. 81% of these marks indicated minima parts, 10% of the marks indicated maxima parts, and 9% of the marks were at other positions. These results provide converging evidence, from two different methods, which supports Hoffman and Richard's minima rule.