Convex Hull Aided Registration Method (CHARM).

ABSTRACTDigital multimedia makes fabricating and copying much easier than ever before. Therefore, it demands efficient and automatic techniques to identify and verify the content of digital multimedia. Image authentication is such a technique to automatically identify whether the query image is a fabrication or a simple copy of the original one. In this paper, we propose a perceptual image authentication technique based on clustering and matching of feature points of images. Feature points are first extracted from images with the k‐largest local total variations and clustered using Fuzzy C‐means clustering algorithm. Then, feature points in the query image and the anchor image are matched into pairs in zigzag ordering along the diagonals of the images cluster by cluster. In the mean time, the outliers of feature points are removed. Then, the system decisions about the authenticity of images are determined by the majority vote of whether three types of distance between matched feature point pairs are larger than their respective thresholds. The three types of distance include the following: (i) histogram‐weighted distance, which is proposed in this paper; (ii) the normalized Euclidean distance; and (iii) the Hausdorff distance. The geometric transform between the query image and the anchor image is estimated, and the query image is registered. The possible tampered image blocks are detected, and the percentage of the tampered area is roughly estimated. The experimental results show the effectiveness and robustness of the proposed image authentication system. Copyright © 2011 John Wiley & Sons, Ltd.

This paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations and under possible occlusion and/or appearance of new objects. It presents a set of local absolute affine invariants derived from the convex hull of scattered feature points (e.g., fiducial or marking points, corner points, inflection points, etc.) extracted from the image. The affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices (quadruplets) of the convex hull, and hence do make direct use of the area invariance property associated with the affine transformation. Because they are locally constructed, they are very well suited to handle the occlusion and/or appearance of new objects. These invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them. A point matching approach for recognition follows this. The time complexity for registering L feature points on the test image with N feature points of the reference image is of order O(N x L). The method has been tested on real indoor and outdoor images and performs well.

3-Points Convex Hull Matching (3PCHM) for fast and robust point set registration

RANdom SAmple Consensus (RANSAC) is widely used in computer vision and automotive related applications. It is an iterative method to estimate parameters of mathematical model from a set of observed data that contains outliers. In computer vision, such observed data is usually a set of features (such as feature points, line segments) extracted from images. In automotive related applications, RANSAC can be used to estimate lane vanishing point, camera rotation angles, ground plane etc. In such applications, changing content of road scene makes stable online model estimation very difficult. In this paper, we propose a framework called tRANSAC to dynamically accumulate features across time so that online RANSAC model estimation can be stably performed. Feature accumulation across time is done in such a dynamic way that when RANSAC tends to perform robustly and stably, accumulated features are discarded fast so that fewer redundant features are used for RANSAC estimation; when RANSAC tends to perform poorly, accumulated features are discarded slowly so that more features can be used for better RANSAC estimation. Experiment results on road scene dataset for camera angle estimation show that the proposed method gives more stable and accurate model compared to baseline method in online RANSAC estimation.

Advances in sensors and cameras allow current research in convex hull algorithms to focus on defining methods capable of processing a big set of points. Typically, in most of these algorithms, the orientation function needs around five sums and two multiplications. In this paper, we propose SymmetricHull, a novel algorithm that, unlike the related ones, only performs two comparisons per point, discarding points with a low probability of belonging to the convex hull. Our algorithm takes advantage of the symmetric geometry of convex hulls in 2D spaces and relies on the convexity principle to get convex hulls, without needing further calculations. Our experiments show that SymmetricHull achieves good results, in terms of time and number of necessary operations, resulting especially efficient with sets of points between \(10^4\) and \(10^7\). Given that our datasets are organized by quadrants, the features of our algorithm can be summarized as follows: (1) a fast point discard based on known points with a good chance to be part of the convex hull, (2) a lexicographic sort of points with a high probability of belonging to the convex hull, and (3) a simple slope analysis to verify whether a point is within the convex hull or not.

This study examines various algorithms for computing the convex hull of a set of n points in a d-dimensional space. Convex hulls are fundamental in computational geometry and are applied in computer graphics, pattern recognition, and computational biology. Such convex hulls can also be useful in symmetry problems. For instance, when points are arranged symmetrically, the convex hull is also likely to be symmetrically shaped, which can be useful for object recognition in computer vision or pattern recognition. The focus is primarily on two-dimensional algorithms, including well-known methods like Gift Wrapping, Graham Scan, Divide and Conquer, QuickHull, TORCH, Kirkpatrick–Sediel, and Chan’s algorithms. These algorithms vary in terms of time complexity and scalability to higher dimensions. This study is extended to three-dimensional convex hull algorithms, such as NAW, randomized insertion, and parallelized versions, such as CudaHull and CudaChain. This study aimed to elucidate the operational principles, step-by-step procedures, and comparative time complexities of each algorithm. The implementation in Python facilitates a detailed comparison of the algorithmic performance through stepwise analysis and graphical outputs. The ultimate goal is to provide insights into the strengths and weaknesses of each algorithm under various scenarios, thereby offering a comprehensive guide for practical implementation.

In the paper, we present and prove Castle Theorem of Convex Hull, design and realize the Fast Rampart Searching Algorithm. The algorithm can be treated as the preprocess of Convex Hull calculation of very large planar point set. When calculating the Convex Hull of a very large planar point set, we can use the Fast Rampart Searching Algorithm to get a very small part points as candidate point set, and then we can get the Convex Hull of the whole planar point set from the candidate point set through other algorithms. Keywords-fast rampart searching algorithm; castle theorem; convex hull; computational geometry

Pilot study of feature-based algorithm for breech face comparison

When an operator teleoperates a rescue robot, it is necessary for the operator to understand the relationship between the robot and its environment while indirect-vision driving. A LRF (Laser Range Finder) installed on a rotating stage is often used for scanning the environment in order to give the operator spatial information, while there is a tradeoff between its scanning speed and point density. To solve the problem, we implement plane detection by RANSAC (RANdom SAmple Consensus) algorithm, integration of overlapped planes using tables and drawing them as convex hulls. The experimental results show that the scanning speed could be improved because the result of 3D scanning with a low point density shows a good match for that with a high point density by using the implemented methods.

Up‐to‐date digital photogrammetry involves operations on huge data sets, and with classical image processing procedures it might be time consuming to find out the best solution. One of the key tasks is to detect outliers in given data, eg for curve fitting or image matching. The problem is hard as the number of outliers is usually large, possibly larger than 50 %, thus powerful estimation techniques are needed. We demonstrate one of these techniques, namely Random Sample Consensus (RANSAC), for fitting a model to sample data, especially for fitting a straight line through a set of given points. Experiments with up to 80 % outliers prove the efficiency of RANSAC. The results are representative for image analysis in digital photogrammetry.

Traditional geometric algorithms are often presented as if input imprecision does not exist, even though it is often unavoidable. We argue that in some cases, it may be desirable for geometric algorithms to treat this imprecision as an explicit component of the input, and to reflect this imprecision in the output. Starting with three problems from computational geometry whose inputs are planar point sets (Voronoi diagrams, convex hulls, and smallest bounding discs), we recast these as problems where each input point’s location is imprecise, but known to lie within a particular region of uncertainty. Where algorithms to solve each of the original problems produce a single geometric object as output, the algorithms that we present typically produce either guaranteed or possible output objects. A guaranteed object represents qualities that can be guaranteed for every point set that is consistent with the uncertain regions, and a possible object represents qualities that exist for at least one such point set. By dealing with input imprecision explicitly, these guaranteed and possible objects can represent a more accurate view of what can be reliably inferred from the input data.

Mixed Integer Linear Programming (MILP) is a very common method of modelling differential and linear bounds. The Convex Hull (CH) modelling, introduced by Sun et al. (Eprint 2013/Asiacrypt 2014), is a popular method in this regard, which can convert the conditions corresponding to a small (4-bit) SBox to MILP constraints efficiently. Our analysis shows, there are SBoxes for which the CH modelling can yield incorrect modelling. The problem arises from the observation that although the CH is generated for a certain set of points, there can be points outside this set which also satisfy all the inequalities of the CH. As apparently no variant of the CH modelling can circumvent this problem, we propose a new modelling for differential and linear bounds. Our modelling makes use of every points of interest individually. Additionally, we also explore the possibility of using redundant constraints, such that the run time for an MILP solver can be reduced while keeping the optimal result unchanged. With our experiments on round-reduced GIFT-128, we show it is possible to reduce the run time a few folds using a suitable choice of redundant constraints. We also present the optimal linear bounds for 11- and 12-rounds of GIFT-128, extending from the best-known result of 10-rounds.

Abstract. In the process of image stitching, the ORB (Oriented FAST and Rotated BRIEF) algorithm lacks the characteristics of scale invariance and high mismatch rate. A principal component invariant feature transform (PCA-ORB, Principal Component Analysis- Oriented) is proposed. FAST and Rotated BRIEF) image stitching method. Firstly, the ORB algorithm is used to optimize the feature points to obtain the feature points with uniform distribution. Secondly, the principal component analysis (PCA) method can reduce the dimension of the traditional ORB feature descriptor and reduce the complexity of the feature point descriptor data. Thirdly, KNN (K-Nearest Neighbor) is used, and the k-nearest neighbor algorithm performs roughly matching on the feature points after dimensionality reduction. Then the random matching consistency algorithm (RANSAC, Random Sample Consensus) is used to remove the mismatched points. Finally, the fading and fading fusion algorithm is used to fuse the images. In 8 sets of simulation experiments, the image stitching speed is improved relative to the PCA-SIFT algorithm. The experimental results show that the proposed algorithm improves the image stitching speed under the premise of ensuring the quality of stitching, and can play a role in fast, real-time and large-scale applications, which are conducive to image fusion.

Image fusion method directly affects the stitching effect. If there are moving objects in the images, the same object may add together after fusion and cause ghosting. A fusion method which can effectively eliminate the exposure difference and ghosting is essential to image mosaic. The method of optimal seam can eliminate integrated ghosting. But the optimal seam may include individual error points and its overall strength value is the smallest. The line is taken as the optimal seam incorrectly. So the ghosting may still exist. In order to avoid the impact of error points an improved optimal seam based on feature point is used in this paper. The scale invariant feature transform and the random sample consensus are used to ensure the detected feature points are accurate. The improved optimal seam do not regard the original optimal seam regards the point with smallest guidelines value as extended direction this paper regards the feature point as the extended direction. The feature point's strength value should have an appropriate weight value. It makes the optimal seam contain more feature points. In this way it can avoid the error points and dynamic elements. Both sides of the optimal seam have exposure differences, an image fusion method should be taken to achieve smooth and natural mosaic. Poisson fusion method can achieve the synthesis of the fragment. So Poisson fusion is used to eliminate exposure difference in this paper.

This paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of [Formula: see text] random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but [Formula: see text] of points can derive the same convex hull as the input set. Finally it will be shown that the running time of the algorithm is [Formula: see text].