Evolutionary algorithms have recently been used to create a wide range of artistic work. In this paper, we propose a new approach for the composition of new images from existing ones, that retain some salient features of the original images. We introduce evolutionary algorithms that create new images based on a fitness function that incorporates feature covariance matrices associated with different parts of the images. This approach is very flexible in that it can work with a wide range of features and enables targeting specific regions in the images. For the creation of the new images, we propose a population-based evolutionary algorithm with mutation and crossover operators based on random walks. Our experimental results reveal a spectrum of aesthetically pleasing images that can be obtained with the aid of our evolutionary process.

The estimation of multiple homographies between two piecewise planar views of a rigid scene is often assumed to be a solved problem. We show that contrary to popular opinion various crucial aspects of the task have not been adequately emphasised. We are motivated by a growing body of literature in robust multi-structure estimation that purports to solve the multi-homography estimation problem but in fact does not. We demonstrate that the estimation of multiple homographies is an ill-solved problem by deriving new constraints that a set of mutually compatible homographies must satisfy, and by showing that homographies estimated with prevailing methods fail to satisfy the requisite constraints on real-world data. We also explain why incompatible homographies imply inconsistent epipolar geometries. The arguments and experiments presented in this paper signal the need for a new generation of robust multi-structure estimation methods that have the capacity to enforce constraints on projective entities such as homography matrices.

It is shown that the set of all I-element collections of interdependent homography matrices describing homographies induced by I planes in the 3D scene between two views has dimension 4I + 7. This improves on an earlier result which gave an upper bound for the dimension in question, and solves a long-standing open problem. The significance of the present result lies in that it is critical to the identification of the full set of constraints to which collections of interdependent homography matrices are subject, which in turn is critical to the design of constrained optimisation techniques for estimating such collections from image data.

The paper presents mathematical underpinnings of the locally linear embedding technique for data dimensionality reduction. It is shown that a cogent framework for describing the method is that of optimization on a Grassmann manifold. The solution delivered by the algorithm is characterized as a constrained minimizer for a problem in which the cost function and all the constraints are defined on such a manifold. The role of the internal gauge symmetry in solving the underlying optimization problem is illuminated.

Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here, it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators, including the renormalization method of Kanatani and the normalized eight-point method of Hartley.

Recovery of dynamic scene properties from multiple videos usually requires the manipulation of synchronous (simultaneously captured) frames. This paper is concerned with the automated determination of this synchrony when the temporal alignment of sequences is unknown. A cost function characterising departure from synchrony is first evolved for the case in which two videos are generated by cameras that may be moving. A novel voting method is then presented for minimising the cost function in the case where the ratio of the cameras' frame rates is unknown. Experimental results indicate this relatively general approach holds promise.

Hartley's eight-point algorithm has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eight-point algorithm that results from using normalized data. It is first established that the normalized algorithm acts to minimize a specific cost function. It is then shown that this cost function I!; statistically better founded than the cost function associated with the nonnormalized algorithm. This augments the original argument that improved performance is due to the better conditioning of a pivotal matrix. Experimental results are given that support the adopted approach. This work continues a wider effort to place a variety of estimation techniques within a coherent framework.

In recent work the authors proposed a wide-ranging method for estimating parameters that constrain image feature locations and satisfy a constraint not involving image data. The present work illustrates the use of the method with experiments concerning estimation of the fundamental matrix. Results are given for both synthetic and real images. It is demonstrated that the method gives results commensurate with, or superior to, previous approaches, with the advantage of being fast.

We present a novel method for estimating the fundamental matrix, a key problem arising in stereo vision. The method aims to minimise a cost function that is derived from maximum likelihood considerations. The respective minimiser turns out to be significantly more accurate than the familiar algebraic least squares technique. Furthermore, the method is identical in accuracy to a Levenberg-Marquardt minimiser, while proving simpler and faster.

A new parameter estimation method is presented, applicable to many com-puter vision problems. It operates under the assumption that the data (typi-cally image point locations) are accompanied by covariance matrices charac-terising data uncertainty. An MLE-based cost function is first formulated and a new minimisation scheme is then developed. Unlike Sampson’s method or the renormalisation technique of Kanatani, the new scheme has as its theoret-ical limit the true minimum of the cost function. It also has the advantages of being simply expressed, efficient, and unsurpassed in our comparative test-ing. 1

We consider the problem of estimating parameters of a model described by an equation of special form. Specific models arise in the analysis of a wide class of computer vision problems, including conic fitting and estimation of the fundamental matrix. We assume that noisy data are accompanied by (known) covariance matrices characterizing the uncertainty of the measurements. A cost function is first obtained by considering a maximum-likelihood formulation and applying certain necessary approximations that render the problem tractable. A Newton-like iterative scheme is then generated for determining a minimizer of the cost function. Unlike alternative approaches such as Sampson's method or the renormalization technique, the new scheme has as its theoretical limit the minimizer of the cost function. Furthermore, the scheme is simply expressed, efficient, and unsurpassed as a general technique in our testing. An important feature of the method is that it can serve as a basis for conducting theoretical comparison of various estimation approaches.

A direct method for the recovery of surface shape from image shading is presented. The method in its basic form is applicable to shading patterns obtained when a distant overhead point light-source illuminates a convex or concave Lambertian surface possessing a single extremal point at which surface height has either a local maximum or local minimum. A key quality of the method is its ability to operate without explicit prerequisite information concerning the shape of the sought-after surface. Consideration is also given to the manipulation of images of more complex surface shapes.