Skeleton pruning as trade-off between skeleton simplicity and reconstruction error

The position and orientation of moving platform mainly depends on global positioning system and inertial navigation system in the field of low-altitude surveying, mapping and remote sensing and land-based mobile mapping system. However, GPS signal is unavailable in the application of deep space exploration and indoor robot control. In such circumstances, image-based methods are very important for self-position and orientation of moving platform. Therefore, this paper firstly introduces state of the art development of the image-based self-position and orientation method (ISPOM) for moving platform from the following aspects: 1) A comparison among major image-based methods (i.e., visual odometry, structure from motion, simultaneous localization and mapping) for position and orientation; 2) types of moving platform; 3) integration schemes of image sensor with other sensors; 4) calculation methodology and quantity of image sensors. Then, the paper proposes a new scheme of ISPOM for mobile robot — depending merely on image sensors. It takes the advantages of both monocular vision and stereo vision, and estimates the relative position and orientation of moving platform with high precision and high frequency. In a word, ISPOM will gradually speed from research to application, as well as play a vital role in deep space exploration and indoor robot control.     

Topological Repairing of 3D Digital Images

We present here a new randomized algorithm for repairing the topology of objects represented by 3D binary digital images. By “repairing the topology”, we mean a systematic way of modifying a given binary image in order to produce a similar binary image which is guaranteed to be well-composed. A 3D binary digital image is said to be well-composed if, and only if, the square faces shared by background and foreground voxels form a 2D manifold. Well-composed images enjoy some special properties which can make such images very desirable in practical applications. For instance, well-known algorithms for extracting surfaces from and thinning binary images can be simplified and optimized for speed if the input image is assumed to be well-composed. Furthermore, some algorithms for computing surface curvature and extracting adaptive triangulated surfaces, directly from the binary data, can only be applied to well-composed images. Finally, we introduce an extension of the aforementioned algorithm to repairing 3D digital multivalued images. Such an algorithm finds application in repairing segmented images resulting from multi-object segmentations of other 3D digital multivalued images.

Preserving Topology by a Digitization Process

The main task of digital image processing is to recognize properties of real objects based on their digital images. These images are obtained by some sampling device, like a CCD camera, and represented as finite sets of points that are assigned some value in a gray-level or color scale. Based on technical properties of sampling devices, these points are usually assumed to form a square grid and are modeled as finite subsets of Z². Therefore, a fundamental question in digital image processing is which features in the digital image correspond, under certain conditions, to properties of the underlying objects. In practical applications this question is mostly answered by visually judging the obtained digital images. In this paper we present a comprehensive answer to this question with respect to topological properties. In particular, we derive conditions relating properties of real objects to the grid size of the sampling device which guarantee that a real object and its digital image are topologically equivalent. These conditions also imply that two digital images of a given object are topologically equivalent. This means, for example, that shifting or rotating an object or the camera cannot lead to topologically different images, i.e., topological properties of obtained digital images are invariant under shifting and rotation.     

Shape similarity measure based on correspondence of visual parts

A cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2D objects. To reduce influence of digitization noise, as well as segmentation errors, the shapes are simplified by a novel process of digital curve evolution. To compute our similarity measure, we first establish the best possible correspondence of visual parts (without explicitly computing the visual parts). Then, the similarity between corresponding parts is computed and aggregated. We applied our similarity measure to shape matching of object contours in various image databases and compared it to well-known approaches in the literature. The experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions.     

A Unified Curvature Definition for Regular,Polygonal, and Digital Planar Curves

In this paper, we propose a new definition of curvature, called visual curvature. It is based on statistics of the extreme points of the height functions computed over all directions. By gradually ignoring relatively small heights, a multi-scale curvature is obtained. The theoretical properties and the experiments presented demonstrate that multi-scale visual curvature is stable, even in the presence of significant noise. To our best knowledge, the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves. Moreover, it yields stable curvature estimates of curves in digital images even under sever distortions. We also show a relation between multi-scale visual curvature and convexity of simple closed curves.     

Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution

We concentrate here on decomposition of 2D objects into meaningfulparts of visual form, orvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution. We obtain a novel rule for decomposition of 2D objects into visual parts, called the hierarchical convexity rule, which states that visual parts are enclosed by maximal convex (with respect to the object) boundary arcs at different stages of the contour evolution. This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of the evolution hierarchy induce a hierarchical structure of the visual parts. The more advanced the stage of contour evolution, the more significant is the shape contribution of the obtained visual parts.     

Face recognition via fast dense correspondence

Face recognition plays a significant role in computer vision. It is well know that facial images are complex stimuli signals that suffer from non-rigid deformations, including misalignment, orientation, pose changes, and variations of facial expression, etc. In order to address these variations, this paper introduces an improved sparse-representation based face recognition method, which constructs dense pixel correspondences between training and testing facial samples. Specifically, we first construct a deformable spatial pyramid graph model that simultaneously regularizes matching consistency at multiple spatial extents - ranging from an entire image, though coarse grid cells, to every single pixel. Secondly, a matching energy function is designed to perform face alignment based on dense pixel correspondence, which is very effective to address the issue of non-rigid deformations. Finally, a novel coarse-to-fine matching scheme is designed so that we are able to speed up the optimization of the matching energy function. After the training samples are aligned with respect to testing samples, an improved sparse representation model is employed to perform face recognition. The experimental results demonstrate the superiority of the proposed method over other methods on ORL, AR, and LFWCrop datasets. Especially, the proposed approach improves nearly 4.4 % in terms of recognition accuracy and runs nearly 10 times faster than previous sparse approximation methods.     

Detection and recognition of contour parts based on shape similarity

Due to distortion, noise, segmentation errors, overlap, and occlusion of objects in digital images, it is usually impossible to extract complete object contours or to segment the whole objects. However, in many cases parts of contours can be correctly reconstructed either by performing edge grouping or as parts of boundaries of segmented regions. Therefore, recognition of objects based on their contour parts seems to be a promising as well as a necessary research direction.The main contribution of this paper is a system for detection and recognition of contour parts in digital images. Both detection and recognition are based on shape similarity of contour parts. For each contour part produced by contour grouping, we use shape similarity to retrieve the most similar contour parts in a database of known contour segments. A shape-based classification of the retrieved contour parts performs then a simultaneous detection and recognition.An important step in our approach is the construction of the database of known contour segments. First complete contours of known objects are decomposed into parts using discrete curve evolution. Then, their representation is constructed that is invariant to scaling, rotation, and translation.     

Dense Neighborhoods on Affinity Graph

In this paper, we study the problem of how to reliably compute neighborhoods on affinity graphs. The k-nearest neighbors (kNN) is one of the most fundamental and simple methods widely used in many tasks, such as classification and graph construction. Previous research focused on how to efficiently compute kNN on vectorial data. However, most real-world data have no vectorial representations, and only have affinity graphs which may contain unreliable affinities. Since the kNN of an object o is a set of k objects with the highest affinities to o, it is easily disturbed by errors in pairwise affinities between o and other objects, and also it cannot well preserve the structure underlying the data. To reliably analyze the neighborhood on affinity graphs, we define the k-dense neighborhood (kDN), which considers all pairwise affinities within the neighborhood, i.e., not only the affinities between o and its neighbors but also between the neighbors. For an object o, its kDN is a set kDN(o) of k objects which maximizes the sum of all pairwise affinities of objects in the set {o}∪kDN(o). We analyze the properties of kDN, and propose an efficient algorithm to compute it. Both theoretic analysis and experimental results on shape retrieval, semi-supervised learning, point set matching and data clustering show that kDN significantly outperforms kNN on affinity graphs, especially when many pairwise affinities are unreliable.