First Type Of Algorithms Research Articles

Review of pedestrian detection technology based on deep learning

Pedestrian detection is one of the main research problems in the field of computer vision. With the development of deep learning technology, pedestrian detection algorithms have made great progress and breakthroughs. Currently, pedestrian detection technology using deep learning has become mainstream. The first type of algorithm is called two-stage detection algorithms, which are based on Region of Interest (ROI) and single-stage detection algorithms adopt an end-to-end training method. So this paper conducts extensive research on the basis of classification and comparison, studies the characteristics and development of the above two detection algorithms, respectively, and finally puts forward suggestions for their future development, such as the fusion of image background and target state.

Fast algorithms for robust principal component analysis with an upper bound on the rank

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular values of a matrix to obtain a low-rank matrix. However, calculating singular values can be very expensive for large matrices. The second type of algorithm replaces the low-rank matrix as the multiplication of two small matrices. They are faster than the first type because no singular value decomposition (SVD) is required. However, the rank of the low-rank matrix is required, and an accurate rank estimation is needed to obtain a reasonable solution. In this paper, we propose algorithms that combine both types. Our proposed algorithms require an upper bound of the rank and SVD on small matrices. First, they are faster than the first type because the cost of SVD on small matrices is negligible. Second, they are more robust than the second type because an upper bound of the rank instead of the exact rank is required. Furthermore, we apply the Gauss-Newton method to increase the speed of our algorithms. Numerical experiments show the better performance of our proposed algorithms.

Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion

In this paper we review several algorithms for image inpainting based on the hypoelliptic diffusion naturally associated with a mathematical model of the primary visual cortex. In particular, we present one algorithm that does not exploit the information of where the image is corrupted, and others that do it. While the first algorithm is able to reconstruct only images that our visual system is still capable of recognize, we show that those of the second type completely transcend such limitation providing reconstructions at the state-of-the-art in image inpainting. This can be interpreted as a validation of the fact that our visual cortex actually encodes the first type of algorithm.

Path Planning Algorithms for Skid-to-Turn Unmanned Aerial Vehicles

This study describes two types of algorithms for skid-to-turn unmanned aerial vehicles to plan paths between two waypoints under constant wind conditions. The first type of algorithm is a rigorous optimization algorithm based on the Euler-Lagrange formulation with analytical integration of the path. The second type of algorithm is a fast algorithm describing the path by two circular arcs connected by a line segment or another circular arc in the air mass frame, which is similar to the Dubins path. The latter algorithm is developed for actual airborne application, whereas the former algorithm is developed to check the quasi-optimality of the path calculated by the latter algorithm. We present a convergence proof of the latter algorithm under certain assumptions and its quasi-optimality in comparison with the former algorithm. Furthermore, the computational efficiency and the convergence reliability of the latter algorithm are demonstrated through numerical examples.

Deterministic Pivoting Algorithms for Constrained Ranking and Clustering Problems

We consider ranking and clustering problems related to the aggregation of inconsistent information, in particular, rank aggregation, (weighted) feedback arc set in tournaments, consensus and correlation clustering, and hierarchical clustering. Ailon et al. [Ailon, N., M. Charikar, A. Newman. 2005. Aggregating inconsistent information: Ranking and clustering. Proc. 37th Annual ACM Sympos. Theory Comput. (STOC '05), 684–693], Ailon and Charikar [Ailon, N., M. Charikar. 2005. Fitting tree metrics: Hierarchical clustering and phylogeny. Proc. 46th Annual IEEE Sympos. Foundations Comput. Sci. (FOCS '05), 73–82], and Ailon [Ailon, N. 2007. Aggregation of partial rankings, p-ratings and top-m lists. Proc. 18th Annual ACM-SIAM Sympos. Discrete Algorithms (SODA '07), 415–424] proposed randomized constant factor approximation algorithms for these problems, which recursively generate a solution by choosing a random vertex as “pivot” and dividing the remaining vertices into two groups based on the pivot vertex. In this paper, we answer an open question in these works by giving deterministic approximation algorithms for these problems. The analysis of our algorithms is simpler than the analysis of the randomized algorithms. In addition, we consider the problem of finding minimum-cost rankings and clusterings that must obey certain constraints (e.g., an input partial order in the case of ranking problems), which were introduced by Hegde and Jain [Hegde, R., K. Jain. 2006. Personal communication]. We show that the first type of algorithms we propose can also handle these constrained problems. In addition, we show that in the case of a rank aggregation or consensus clustering problem, if the input rankings or clusterings obey the constraints, then we can always ensure that the output of any algorithm obeys the constraints without increasing the objective value of the solution.

Volume of intersection of two cones

Radiation measurements utilising collimated source and detector systems invariably result in a target volume described by the overlap of their fields of view. When these collimators are cylindrical, this is derived from the volume of intersection of two cones. In general, analysis of this volume does not lend itself to a direct analytical process. Here, numerical methods of estimating the common volume of two intersecting right cones are presented. These include methods which employ, (a) a sequential scanning of an elemental volume with a predetermined size across a defined space containing the volume of interest and (b) a Monte Carlo technique. The accuracy obtainable and the execution time in the first type of algorithm depend on the size of the elemental volume (bin-size). On the other hand, these two parameters are independent of the bin-size but dependent on the number of histories sampled, for the Monte Carlo technique. At 0° angle of inclination, where an analytical estimation is easily obtained, the three algorithms considered here resulted in values with a precision better than 0.1% when compared to the analytically calculated one.

Algorithms for Colouring Random k-colourable Graphs

The k-colouring problem is to colour a given k-colourable graph with k colours. This problem is known to be NP-hard even for fixed k [ges ] 3. The best known polynomial time approximation algorithms require nδ (for a positive constant δ depending on k) colours to colour an arbitrary k-colourable n-vertex graph. The situation is entirely different if we look at the average performance of an algorithm rather than its worst-case performance. It is well known that a k-colourable graph drawn from certain classes of distributions can be k-coloured almost surely in polynomial time.In this paper, we present further results in this direction. We consider k-colourable graphs drawn from the random model in which each allowed edge is chosen independently with probability p(n) after initially partitioning the vertex set into k colour classes. We present polynomial time algorithms of two different types. The first type of algorithm always runs in polynomial time and succeeds almost surely. Algorithms of this type have been proposed before, but our algorithms have provably exponentially small failure probabilities. The second type of algorithm always succeeds and has polynomial running time on average. Such algorithms are more useful and more difficult to obtain than the first type of algorithms. Our algorithms work as long as p(n) [ges ] n−1+ε where ε is a constant greater than 1/4.

Algorithms for coloring semi-random graphs

The graph coloring problem is to color a given graph with the minimum number of colors. This problem is known to be NP-hard even if we are only aiming at approximate solutions. On the other hand, the best known approximation algorithms require $n^\delta (\delta>0)$ colors even for bounded chromatic k-colorable for fixed k n-vertex graphs. The situation changes dramatically if we look at the average performance of an algorithm rather than its worst case performance. A k-colorable graph drawn from certain classes of distributions can be k-colored almost surely in polynomial time. It is also possible to k-color such random graphs in polynomial average time. In this paper, we present polynomial time algorithms for k-coloring graphs drawn from the semirandom model. In this model, the graph is supplied by an adversary each of whose decisions regarding inclusion of edges is reversed with some probability p. In terms of randomness, this model lies between the worst case model and the usual random model where each edge is chosen with equal probability. We present polynomial time algorithms of two different types. The first type of algorithms w always run in polynomial time and succeed almost surely. Blum and Spencer [J. Algorithms, 19, 204-234 1995] have also obtained independently such algorithms, but our results are based on different proof techniques which are interesting in their own right. The second type of algorithms always succeed and have polynomial running time on the average. Such algorithms are more useful and more difficult to obtain than the first type of algorithms. Our algorithms work for semirandom graphs drawn from a wide range of distributions and work $p \ge n^{-{\alpha (k)}+\epsilon}}$ Where $\alpha(k) = \frac{(2k)}{((k-1)(k+2))}$ and \epsilon is a positive constant.

Optimization Methods for Discontinuous and Smooth Controls in Semi-Linear Hyperbolic Systems

Two types of algoritms of optimization of controlled processes described by semi-linear hyperbolic equations systems are suggested in this paper. The first type of algorithms is based on the analogue of L.S. Pontryagin's needle variation and its convergence is realized in the sense of tendency to the maximum principle. The second type of algorithms is constructed basing on the analogue of inner variation. This algorithm is considered for hyperbolic systems with additional integral constraints. Neither techniques of Lagrange multipliers nor ideas of penalty functions are used, although they are usually applied to solve optimization problems with additional constraints. The algorithm converges to new necessary conditions of optimality.

The adjoining cell mapping and its recursive unraveling, part I: Description of adaptive and recursive algorithms

A new type of cell mapping, referred to as an adjoining cell mapping, is developed in this paper for autonomous dynamical systems employing the cellular state space. It is based on an adaptive time integration employed to compute an associated cell mapping for the system. This technique overcomes the problem of determining an appropriate duration of integration time for the simple cell mapping method. Employing the adjoining mapping principle, the first type of algorithm developed here is an adaptive mapping unraveling algorithm to determine equilibria and limit cycles of the dynamical system in a way similar to that of the simple cell mapping. In addition, it is capable of providing useful information regarding the behavior of dynamical systems possessing pathological dynamics and of systems with rapidly changing vector field. The adjoining property inherent in the adjoining cell mapping method, in general, permits development of new recursive algorithms for unraveling dynamics. The required computer memory for a practical implementation of such algorithms is considerably less than that required by the simple cell mapping algorithm since they allow for a recursive partitioning of state space for trajectory analysis. The second type of algorithm developed in this paper is a recursive unraveling algorithm based on adaptive integration and recursive partitioning of state space into blocks of cells with a view toward its practical implementation. It can find equilibria of the system in the same manner as the simple cell mapping method but is more efficient in locating periodic solutions.