Monte Carlo Estimation of a Joint Density Using Malliavin Calculus, and Application to American Options

We use the Malliavin integration by parts formula in order to provide a family of representations of the joint density (which does not involve Dirac measures) of (X_θ, X _{θ + δ}), where X is a d-dimensional Markov diffusion (d ≥ 1), θ > 0 and δ > 0. Following Bouchard et al. (2004), the different representations are determined by a pair of localizing functions. We discuss the problem of variance reduction within the family of separable localizing functions: We characterize a pair of exponential functions as the unique integrated-variance minimizer among this class of separable localizing functions. We test our method on the d-dimensional Brownian motion and provide an application to the problem of American options valuation by the quantization tree method introduced by Bally et al. (2002). MSC 1991 Subject Classifications: Primary 60H07 65C05, secondary 49-00     

A mixed finite-element finite-difference method to solve the equilibrium equations of a prestressed membrane having boundary cables

This paper proposes a mathematical method to solve the equilibrium equations of a membrane with rigid and cable boundaries for the so-called prestressing phase. More exactly, no constrained thrust network approach is implemented and the problem is studied starting directly from its continuous formulation. In this sense, the membrane is represented by a regular surface with negative Gaussian curvature, and its boundary by a set of regular curves, whose curvature depends on the structural elements, rigid or cable. The equilibrium is expressed by means of boundary differential problems in terms of the membrane shape and its stress tensor. The membrane-cable interface equilibrium requires taking into account a singular condition which makes the problem more complex. Therefore, the corresponding mathematical problem is defined and analysed, and its principal qualitative aspects are discussed in this paper. Moreover, a numerical resolution procedure is proposed and applied.     

A survey of genetic algorithm-based face recognition

Traditionally, special objects can be detected and recognized by the template matching method, but the recognition speed has always been a problem. In addition, for recognition by a neural network, training the data is always time-consuming. In this article, the current method of genetic algorithm-based face recognition is summarized, and experiments for real-time use are described. The chromosomes generated by the genetic algorithm (GA) contain information (parameters) about the face, and genetic operators are used to detect and obtain the position of the face of interest in an image. Here, the parameters of the coordinates (x, y) of the center of the face, the rate of scale, and the angle of rotation θ, are encoded into the GA.     

Color reconstruction in digital cameras: optimization for document images

Digital cameras normally sample one color at each pixel. Missing colors are obtained by spatial interpolation, decreasing resolution relative to images acquired with a greyscale sensor. The consequence for document imaging is higher text recognition error rates. This paper introduces the horizontal-vertical regression (HVR) method for document-optimized color reconstruction. HVR exploits a local two-color approximation, making spatial interpolation unnecessary. Comparison with the best alternative reconstruction methods indicates large reductions in error rates for text resulting from HVR, as well as improvements in intermediate color and binary images.Received: 11 June 2003, Accepted: 6 March 2004, Published online: 2 February 2005C. Dance: Correspondence to     

A color object recognition scheme: application to cellular sorting

This paper presents a color object recognition scheme which proceeds in three sequential steps: segmentation, features extraction and classification. We mainly focus on the first and the third steps here. A color watershed using global and local criteria is first described. A color contrast value is defined to select the best color space for segmenting color objects. Then, an architecture of binary neural networks is described. Its properties relies on the simplification of the recognition problem, leading to a noticeable increase in the classification rate. We conclude with the abilities of such a recognition scheme and present an automated cell sorting system. Received: 15 June 2001 / Accepted: 1 July 2002 Published online: 23 April 2003 Correspondence to: O. Lezoray (e-mail: Olivier.Lezoray@info.unicaen.fr)     

Automated delineation of individual tree crowns in high spatial resolution aerial images by multiple-scale analysis

This paper presents an automatic multiple-scale algorithm for delineation of individual tree crowns in high spatial resolution infrared colour aerial images. The tree crown contours were identified as zero-crossings, with convex grey-level curvature, which were computed on the intensity image for each image scale. A modified centre of curvature was estimated for every edge segment pixel. For each segment, these centre points formed a swarm which was modelled as a primal sketch using an ellipse extended with the mean circle of curvature. The model described the region of the derived tree crown based on the edge segment at the current scale. The sketch was rescaled with a significance value and accumulated for a scale interval. In the accumulated sketch, a tree crown segment was grown, starting at local peaks, under the condition that it was inside the area of healthy vegetation in the aerial image and did not trespass into a neighbouring crown segment. The method was evaluated by comparison with manual delineation and with ground truth on 43 randomly selected sample plots. It was concluded that the performance of the method is almost equivalent to visual interpretation. On the average, seven out of ten tree crowns were the same. Furthermore, ground truth indicated a large number of hidden trees. The proposed technique could be used as a basic tool in forest surveys. Received: 24 June 1997 / Accepted: 28 April 1998     

Efficient parallel algorithms for computing all pair shortest paths in directed graphs

We present parallel algorithms for computing all pair shortest paths in directed graphs. Our algorithm has time complexityO(f(n)/p+I(n)logn) on the PRAM usingp processors, whereI(n) is logn on the EREW PRAM, log logn on the CCRW PRAM,f(n) iso(n ³). On the randomized CRCW PRAM we are able to achieve time complexityO(n ³/p+logn) usingp processors. A preliminary version of this paper was presented at the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, June 1992. Support by NSF Grant CCR 90-20690 and PSC CUNY Awards #661340 and #662478.     

Perito Moreno Glacier (Argentina) flow estimation by COSMO SkyMed sequence of high-resolution SAR-X imagery

The Perito Moreno Glacier (Los Glaciares National Park, Patagonia, Argentina) ice stream has been investigated using X-band SAR amplitude images collected from February to December 2009 (excluding June) at time intervals of 8 and 16 days by the COSMO SkyMed satellites. The high spatial resolution dataset (10 × 10 km swath, 1 m per pixel) reveals many details of the glacier surface and the ice velocity fields extracted from sequential image pairs by the maximum cross-correlation method cover most of the glacier area. The efficiency of the cross-correlation method improves with high spatial resolution imagery and the co-registration error of the image pair also reduces. The glacier motion detected in the period shows variability on the time scale considered, evidencing the areas of higher dynamics under different speed regimes.     

A study of capillary flow from a pendant droplet

Surface tension driven capillary flow from a pendant droplet into a horizontal glass capillary is investigated in this paper. Effect of the droplet surface on dynamic behavior of such capillary flow is examined and compared with surface tension driven capillary flow from an infinite reservoir. In the experiment, capillaries of 300–700 μm in diameter were used with glycerol–DI water mixture solutions having viscosities ranging from 80 to 934 mPa s. It is observed that compared to the capillary flow from an infinite reservoir, the capillary flow from a droplet exhibits higher rates of meniscus displacement. This is due to an additional driving force resulted from change in droplet surface area (or curvature). The two main parameters influencing the flow are the dimensionless droplet geometry parameter (k) and the dynamic contact angle (θ _D). The molecular kinetics theory of Blake and De Coninck’s model [Adv Colloid Interface Sci 96(1–3):21–36, 2002] is used to interpret the dynamic contact angle. This theory considers a molecular friction coefficient (ζ) at the liquid front flowing over a solid surface. Moreover, three models are proposed to describe the shape of the pendant droplet during capillary action. It is found that the egg-shaped model provides a more realistic model to compute the shape of the pendant droplet deformed during the capillary action. Thus the predictions by the egg-shaped model are in good agreement with the experimental data.     

Non-smooth simultaneous stabilization of nonlinear systems: An interpolation method

In this paper, we introduce a method which enables us to construct a continuous simultaneous stabilizer for pairs of systems in which cannot be simultaneously stabilized by means of C¹ feedback. We extend this method to higher-dimensional systems and show that any pair of asymptotically stabilizable nonlinear systems can be simultaneously stabilized (not asymptotically) by means of continuous feedback.     

3D motion estimation of bubbles of gas in fluid glass,using an optical flow gradient technique extended to a third dimension

To solve the problem of estimating velocities of gas bubbles in melted glass, a method based on optical flow constraint (OFC) has been extended to the 3D case. A single camera, whose distance to the fluid is variable in time, is used to capture a sequence of frames at different depths. Since objects are not static, we cannot obtain two frames of different height values at the same time, and to our knowledge, this prevents the use of common 3D motion estimation techni ques. Since the information will be rather sparse, our estimation takes several measures around a given pixel and discards the erroneous ones, using a robust estimator. Along with the exposition of the practical application, the estimation proposed here is first contrasted in the 2D case to common benchmarks and then evaluated for a synthetic problem where velocities are known. Received: 9 July 2001 / Accepted: 5 August 2002 Published online: 3 June 2003 This work has been supported by Saint Gobain Cristaleria S.A., under contract FUO-EM-034-01 with Oviedo University, Spain.     

Anisotropic Filtering of Non-Linear Surface Features

A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non‐linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well‐known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non‐linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.     

Practical and flexible path planning for car-like mobile robot using maximal-curvature cubic spiral

This paper presents a nonholonomic path planning method, aiming at taking into considerations of curvature constraint, length minimization, and computational demand, for car-like mobile robot based on cubic spirals. The generated path is made up of at most five segments: at most two maximal-curvature cubic spiral segments with zero curvature at both ends in connection with up to three straight line segments. A numerically efficient process is presented to generate a Cartesian shortest path among the family of paths considered for a given pair of start and destination configurations. Our approach is resorted to minimization via linear programming over the sum of length of each path segment of paths synthesized based on minimal locomotion cubic spirals linking start and destination orientations through a selected intermediate orientation. The potential intermediate configurations are not necessarily selected from the symmetric mean circle for non-parallel start and destination orientations. The novelty of the presented path generation method based on cubic spirals is: (i) Practical: the implementation is straightforward so that the generation of feasible paths in an environment free of obstacles is efficient in a few milliseconds; (ii) Flexible: it lends itself to various generalizations: readily applicable to mobile robots capable of forward and backward motion and Dubins’ car (i.e. car with only forward driving capability); well adapted to the incorporation of other constraints like wall-collision avoidance encountered in robot soccer games; straightforward extension to planning a path connecting an ordered sequence of target configurations in simple obstructed environment.     

Low-cost interactive active range finder

This paper describes a new type of low-cost interactive active range finder and illustrates the effect of introducing interactivity to the range-acquisition process. The new range finder consists of only one camera and a laser pointer to which three LEDs are attached. When a user scans the laser, the camera captures the image of spots (one from the laser and the others from LEDs), and triangulation is carried out using the camera's viewing direction and the optical axis of the laser. The user interaction allows the range finder to acquire range data in which the sampling rate varies across the object depending on the underlying surface structures. Moreover, the processes of separating objects from the background and/or finding parts in the object can be achieved using the operator's knowledge of the objects. Received: 24 August 1999 / Accepted: 26 May 2000 Published online: 18 June 2003 Correspondence to: M. Takatsuka (e-mail: masa@it.usyd.edu.au) This project was funded by a grant from the Australian Research Council.     

Motion estimation methods and noisy phenomena

In an infrared surveillance system (which must detect remote sources and thus has a very low resolution) in an aerospace environment, the estimation of the cloudy sky velocity should lower the false alarm rate in discriminating the motion between various moving shapes by means of a background velocity map. The optical flow constraint equation, based on a Taylor expansion of the intensity function, is often used to estimate the motion for each pixel. One of the main problems in motion estimation is that, for one pixel, the real velocity cannot be found because of the aperture problem. Another kinematic estimation method is based on a matched filter [generalized Hough transform (GHT)]: it gives a global velocity estimation for a set of pixels. On the one hand we obtain a local velocity estimation for each pixel with little credibility because the optical flow is so sensitivity to noise; on the other hand, we obtain a robust global kinematic estimation, the same for all selected pixels. This paper aims to adapt and improve the GHT in our typical application in which one must discern the global movement of objects (clouds), whatever their form may be (clouds with hazy edges or distorted shapes or even clouds that have very little structure). We propose an improvement of the GHT algorithm by segmentation images with polar constraints on spatial gradients. One pixel, at timet, is matched with another one at timet + T, only if the direction and modulus of the gradient are similar. This technique, which is very efficient, sharpens the peak and improves the motion resolution. Each of these estimations is calculated within windows belonging to the image, these windows being selected by means of an entropy criterion. The kinematic vector is computed accurately by means of the optical flow constraint equation applied on the displaced window. We showed that, for small displacements, the optical flow constraint equation sharpens the results of the GHT. Thus a semi-dense velocity field is obtained for cloud edges. A velocity map computed on real sequences with these methods is shown. In this way, a kinematic parameter discriminates between a target and the cloudy background.     

Rapid omnidirectional vision acquisition using an intelligent linear scanning technique

Many computer vision applications can benefit from omnidirectional vision sensing, rather than depending solely on conventional cameras that have constrained fields of view. For example, mobile robots often require a full 360 view of their environment in order to perform navigational tasks such identifying landmarks, localizing within the environment, and determining free paths in which to move. There has been much research interest in omnidirectional vision in the past decade and many techniques have been developed. These techniques include: (i) catadioptric methods which can provide rapid image acquisition, but lack image resolution; and (ii) mosaicing and linear scanning techniques which have high image resolution but typically have slow image acquisition speed. In this paper, we introduce a novel linear scanning panoramic vision system that can acquire panoramic images quickly with little loss of image resolution. The system makes use of a fast line-scan camera, instead of a slower, conventional area-scan camera. In addition, a unique coarse-to-fine panoramic imaging technique has been developed that is based on smart sensing principles. Using the active vision paradigm, we control the motion of the rotating camera using feedback from the images. This results in high acquisition speeds and proportionally low storage requirements. Experimentation has been carried out, and results are given. Correspondence to: M.J. Barth (e-mail: barth@ee.ucr.edu)     

Invariant surface segmentation through energy minimization with discontinuities

The computational problems in segmenting range data into surface patches based on the invariant surface properties, i.e., mean curvature H and Gaussian curvature K, are investigated. The goal is to obtain reliable HK surface maps. Two commonly encountered problems are: firstly the noise effect in computing derivative estimates, and secondly the smoothing across discontinuities. Here, the segmentation is formulated as finding minimization solutions of energy functionals involving discontinuities. A two-stage approach to the goal is presented: stage (1) from a range image to curvature images and stage (2) from the curvature images to the HK maps. In both stages, solutions are found through minimizing energy functionals that measure the degree of bias of a solution from two constraints: the closeness of the solution to the data, and the smoothness of the solution controlled by predetermined discontinuities. Propagation across discontinuities is prevented during minimization, which preserves the original surface shapes. Experimental results are given for a variety of test images.This work was supported by a TC Scholarship from the British Council.     

Layup optimization against buckling of shear panels

The object of the study was to optimize the shear buckling load of laminated composite plates. The laminates lacked coupling between bending and extension (B _ij=0) but had otherwise arbitrary selection of the ply angle variation through the thickness. The plates were rectangular and either simply supported or clamped on all edges. For orthotropic plates, it was seen that there is only one parameter necessary for finding the optimal design for different materials and plate aspect ratios. This parameter can be interpreted as the layup angle in a (+/–) orthotropic laminate. When bendingtwisting coupling is present, the buckling strength depends on the direction of the applied load. A laminate with non-zero bending-twisting coupling stiffnesses can be described with four lamination parameters. The allowable region of these parameters was investigated, and an optimization of the buckling load within this region was performed. It was seen that even this is a one parameter problem. This parameter can be interpreted as the layup anlge in an off-axis unidirectional laminate ().Notations A _ij in-plane stiffnesses of anisotropic plates, Tsai and Hahn (1980) - B _ij coupling stiffnesses of anisotropic plates - D _ij bending stiffnesses of anisotropic plates - D _ij ^* normalized bending stiffnesses - a, b, h length, width and thickness of the plate - x, y in-plane coordinates - z through-the-thickness coordinate - z ^* normalized through-the-thickness coordinate - w (x, y) out-of-plane deformation - N _xy shear buckling load - W ₁ ^* toW ₄ ^* lamination parameters - U ₁ toU ₅ linear combinations of the on-axis moduli - (z) layup angle - f _k functional of(z)     

New Finite Algorithm for Solving the Generalized Nonhomogeneous Yakubovich‐Transpose Matrix Equation

In this paper, the development of the conjugate direction (CD) method is constructed to solve the generalized nonhomogeneous Yakubovich‐transpose matrix equation AXB + CX^TD + EYF = R. We prove that the constructed method can obtain the (least Frobenius norm) solution pair (X,Y) of the generalized nonhomogeneous Yakubovich‐transpose matrix equation for any (special) initial matrix pair within a finite number of iterations in the absence of round‐off errors. Finally, two numerical examples show that the constructed method is more efficient than other similar iterative methods in practical computation.