On the Geometries of Conic Section Representation of Noisy Object Boundaries

This paper studies some geometrical properties of conic sections and the utilization of these properties for the generation of conic section representations of object boundaries in digital images. Several geometrical features of the conic sections, such as the chord, the characteristic point, the guiding triangles, and their appearances under the tessellation and noise corruption of the digital images are discussed. The study leads to a noniterative algorithm that takes advantage of these features in the process of formulating the conic section parameters and generating the approximations of object boundaries from the given sequences of edge pixels in the images. The results can be optimized with respect to certain different criteria of the fittings

Real-World Normal Map Capture for Nearly Flat Reflective Surfaces

Although specular objects have gained interest in recent years, virtually no approaches exist for markerless reconstruction of reflective scenes in the wild. In this work, we present a practical approach to capturing normal maps in real-world scenes using video only. We focus on nearly planar surfaces such as windows, facades from glass or metal, or frames, screens and other indoor objects and show how normal maps of these can be obtained without the use of an artificial calibration object. Rather, we track the reflections of real-world straight lines, while moving with a hand-held or vehicle-mounted camera in front of the object. In contrast to error-prone local edge tracking, we obtain the reflections by a robust, global segmentation technique of an ortho-rectified 3D video cube that also naturally allows efficient user interaction. Then, at each point of the reflective surface, the resulting 2D-curve to 3D-line correspondence provides a novel quadratic constraint on the local surface normal. This allows to globally solve for the shape by integrability and smoothness constraints and easily supports the usage of multiple lines. We demonstrate the technique on several objects and facades

Detection of curved edges at subpixel accuracy using deformable models

One approach to the detection of curves at subpixel accuracy involves the reconstruction of such features from subpixel edge data points. A new technique is presented for reconstructing and segmenting curves with subpixel accuracy using deformable models. A curve is represented as a set of interconnected Hermite splines forming a snake generated from the subpixel edge information that minimizes the global energy functional integral over the set. While previous work on the minimization was mostly based on the Euler-Lagrange transformation, the authors use the finite element method to solve the energy minimization equation. The advantages of this approach over the Euler-Lagrange transformation approach are that the method is straightforward, leads to positive m-diagonal symmetric matrices, and has the ability to cope with irregular geometries such as junctions and corners. The energy functional integral solved using this method can also be used to segment the features by searching for the location of the maxima of the first derivative of the energy over the elementary curve set

ARCHITECTURE ESTIMATION FROM SPARSE IMAGES USING GRAMMATICAL SHAPE PRIORS FOR CULTURAL HERITAGE

The estimation and reconstruction of 3D architectural structures is of great in- terest in computer vision, as well as cultural heritage. This dissertation proposes a novel approach to solve the di??cult problem of estimating architectural structures from sparse images and e??ciently generating 3D models from estimation results for cultural heritage. This approach takes as input one plan drawing image and a few fac¸ade images, and provides as output the volumetric 3D models which represent the structures in the sparse images. Support of this research goal has motivated new investigations in underlying structure estimation problems including detecting structural feature points in 2D images, decomposing plan drawings into semantically meaningful shapes for medieval castles, estimating rectangular and Gothic fac¸ades using shape priors, and estimating complete 3D models for architectural structures using a novel volumetric shape grammar. Major outstanding challenges in each of these topic areas are addressed resulting in contributions to current state-of-the-art as it applied to these di??cult problems

Using Lidar to geometrically-constrain signature spaces for physics-based target detection

A fundamental task when performing target detection on spectral imagery is ensuring that a target signature is in the same metric domain as the measured spectral data set. Remotely sensed data are typically collected in digital counts and calibrated to radiance. That is, calibrated data have units of spectral radiance, while target signatures in the visible regime are commonly characterized in units of re°ectance. A necessary precursor to running a target detection algorithm is converting the measured scene data and target signature to the same domain. Atmospheric inversion or compensation is a well-known method for transforming mea- sured scene radiance values into the re°ectance domain. While this method may be math- ematically trivial, it is computationally attractive and is most e®ective when illumination conditions are constant across a scene. However, when illumination conditions are not con- stant for a given scene, signi¯cant error may be introduced when applying the same linear inversion globally. In contrast to the inversion methodology, physics-based forward modeling approaches aim to predict the possible ways that a target might appear in a scene using atmospheric and radiometric models. To fully encompass possible target variability due to changing illumination levels, a target vector space is created. In addition to accounting for varying illumination, physics-based model approaches have a distinct advantage in that they can also incorporate target variability due to a variety of other sources, to include adjacency target orientation, and mixed pixels. Increasing the variability of the target vector space may be beneficial in a global sense in that it may allow for the detection of difficult targets, such as shadowed or partially concealed targets. However, it should also be noted that expansion of the target space may introduce unnecessary confusion for a given pixel. Furthermore, traditional physics-based approaches make certain assumptions which may be prudent only when passive, spectral data for a scene are available. Common examples include the assumption of a °at ground plane and pure target pixels. Many of these assumptions may be attributed to the lack of three-dimensional (3D) spatial information for the scene. In the event that 3D spatial information were available, certain assumptions could be levied, allowing accurate geometric information to be fed to the physics-based model on a pixel- by-pixel basis. Doing so may e®ectively constrain the physics-based model, resulting in a pixel-specific target space with optimized variability and minimized confusion. This body of work explores using spatial information from a topographic Light Detection and Ranging (Lidar) system as a means to enhance the delity of physics-based models for spectral target detection. The incorporation of subpixel spatial information, relative to a hyperspectral image (HSI) pixel, provides valuable insight about plausible geometric con¯gurations of a target, background, and illumination sources within a scene. Methods for estimating local geometry on a per-pixel basis are introduced; this spatial information is then fed into a physics-based model to the forward prediction of a target in radiance space. The target detection performance based on this spatially-enhanced, spectral target space is assessed relative to current state-of-the-art spectral algorithms

Asymptotically efficient estimators for geometric shape fitting and source localization

Solving the nonlinear estimation problem is known to be a challenging task because of the implicit relationship between the measurement data and the unknown parameters to be estimated. Iterative methods such as the Taylor-series expansion based ML estimator are presented in this thesis to solve the nonlinear estimation problem. However, they might suffer from the initialization and convergence problems. Other than the iterative methods, this thesis aims to provide a computational effective, asymptotically efficient and closed-form solution to the nonlinear estimation problem. Two kinds of classic nonlinear estimation problems are considered: the geometric shape fitting problem and the source localization problem. For the geometric shape fitting, the research in this thesis focuses on the circle and the ellipse fittings. Three iterative methods for the fitting of a single circle: the ML method, the FLS method and the SDP method, are provided and their performances are analyzed. To overcome the limitations of the iterative methods, asymptotically efficient and closed-form solutions for both the circle and ellipse fittings are derived. The good performances of the proposed solutions are supported by simulations using synthetic data as well as experiments on real images. The localization of a source via a group of sensors is another important nonlinear estimation problem studied in this thesis. Based on the TOA measurements, the CRLB and MSE results of a source location when sensor position errors are present are derived and compared to show the estimation performance loss due to the sensor position errors. A closed-formed estimator that takes into account the sensor position errors is then proposed. To further improve the sensor position and the source location estimates, an algebraic solution that jointly estimates the source and sensor positions is provided, which provides better performance in sensor position estimates at higher noise level comparing to the sequential estimation-refinement technique. The TOA based CRLB and MSE studies are further extended to the TDOA and AOA cases. Through the analysis one interesting result has been found: there are situations exist where taking into account the sensor position errors when estimating the source location will not improve the estimation accuracy. In such cases a calibration emitter with known position is needed to limit the estimation damage caused by the sensor position uncertainties. Investigation has been implemented to find out where would be the optimum position to place the calibration emitter. When the optimum calibration source position may be of theoretical interest only, a practical suboptimum criterion is developed which yields a better calibration emitter position than the closest to the unknown source criterion

A study of Symmetric and Repetitive Structures in Image-Based Modeling

Ph.DDOCTOR OF PHILOSOPH