A simple and efficient preprocessing step for convex hull problem

The present paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of $n$ random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but $O(\log n)$ 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 $O(n

Extraction of textual information from image for information retrieval

Ph.DDOCTOR OF PHILOSOPH

Technological innovations in the collection and analysis of three-dimensional footwear impression evidence.

The development of digital 3D trace recovery in the fields of geology and archaeology has highlighted transferable methods that could be used for the recovery of 3D footwear impressions under the umbrella of forensic science. This project uses a portfolio of experiments and case studies to explore the veracity and application of SfM Photogrammetry (i.e., DigTrace) within forensic footwear. This portfolio-based research includes published papers integrated into conventional chapters. A method of comparing the accuracy and precision of different measurement methods is developed and introduced and gives a comparative view of multiple recovery techniques. A range of simulated crime scene and laboratory-controlled experiments have been conducted to compare different recovery methods such as casting, photography and SfM photogrammetry. These have been compared for accuracy, practicality and effectiveness. In addition, a range of common and lesser common footwear bearing substrates have been compared using SfM as well as other methods. One of the key findings shows that DigTrace SfM photogrammetry software reliably produces accurate forensic results, regardless of the camera used for initial photography and in a multitude of environments. This includes but is not limited to, soil, sand, snow, and other less obvious substrates such as food items, household items and in particular carpet. The thesis also shows that SfM photogrammetry provides a superior solution in the recovery of ‘difficult to cast’ footwear impressions. This finding allows for 3D recovery of impressions that would otherwise have only been photographed in 2D. More generally this project shows that 3D recovery is preferential to 2D and aids in the identification of individual characteristics and subsequent positive analysis. Overall, the thesis concludes that SfM photogrammetry is a viable and accurate solution for the recovery of 3D footwear impressions both as an alternative and replacement to 2D photography and conventional 3D casting. SfM 3D recovery provides increased visualisation of footwear evidence and individualising marks. Digital evidence obtained in this way integrates with the increasingly sophisticated search algorithms being used within the UK’s National Footwear Database and allows rapid file sharing, retrieval and evidence sharing. Moreover, the technique has significant cost saving in terms of time, equipment and resources. It is the author’s opinion, having consulted a wide audience of footwear examiners and crime scene employees, that this technique should, and can be, adopted quickly by forces in the UK and USA and disseminated for use

Adaptive Modeling of Details for Physically-based Sound Synthesis and Propagation

In order to create an immersive virtual world, it is crucial to incorporate a realistic aural experience that complements the visual sense. Physically-based sound simulation is a method to achieve this goal and automatically provides audio-visual correspondence. It simulates the physical process of sound: the pressure variations of a medium originated from some vibrating surface (sound synthesis), propagating as waves in space and reaching human ears (sound propagation). The perceived realism of simulated sounds depends on the accuracy of the computation methods and the computational resource available, and oftentimes it is not feasible to use the most accurate technique for all simulation targets. I propose techniques that model the general sense of sounds and their details separately and adaptively to balance the realism and computational costs of sound simulations. For synthesizing liquid sounds, I present a novel approach that generate sounds due to the vibration of resonating bubbles. My approach uses three levels of bubble modeling to control the trade-offs between quality and efficiency: statistical generation from liquid surface configuration,explicitly tracking of spherical bubbles, and decomposition of non-spherical bubbles to spherical harmonics. For synthesizing rigid-body contact sounds, I propose to improve the realism in two levels using example recordings: first, material parameters that preserve the inherent quality of the recorded material are estimated; then extra details from the example recording that are not fully captured by the material parameters are computed and added. For simulating sound propagation in large, complex scenes, I present a novel hybrid approach that couples numerical and geometric acoustic techniques. By decomposing the spatial domain of a scene and applying the more accurate and expensive numerical acoustic techniques only in limited regions, a user is able to allocate computation resources on where it matters most.Doctor of Philosoph

Template reduction of feature point models for rigid objects and application to tracking in microscope images.

This thesis addresses the problem of tracking rigid objects in video sequences. A novel approach to reducing the template size of shapes is presented. The reduced shape template can be used to enhance the performance of tracking, detection and recognition algorithms. The main idea consists of pre-calculating all possible positions and orientations that a shape can undergo for a given state space. From these states, it is possible to extract a set of points that uniquely and robustly characterises the shape for the considered state space. An algorithm, based on the Hough transform, has been developed to achieve this for discrete shapes, i.e. sets of points, projected in an image when the state space is bounded. An extended discussion on particle filters, that serves as an introduction to the topic, is presented, as well as some generic improvements. The introduction of these improvements allow the data to be better sampled by incorporating additional measurements and knowledge about the velocity of the tracked object. A partial re-initialisation scheme is also presented that enables faster recovery of the system when the object is temporarily occluded.A stencil estimator is introduced to identify the position of an object in an image. Some of its properties are discussed and demonstrated. The estimator can be efficiently evaluated using the bounded Hough transform algorithm. The performance of the stencilled Hough transform can be further enhanced with a methodology that decimates the stencils while maintaining the robustness of the tracker. Performance evaluations have demonstrated the relevance of the approach. Although the methods presented in this thesis could be adapted to full 3-D object motion, motions that maintain the same view of the object in front of a camera are more specifically studied