The Dual Marching Tetrahedra algorithm is a generalization of the Dual Marching Cubes algorithm, used to build a boundary surface around points which have been assigned a particular scalar density value, such as the data produced by and Magnetic Resonance Imaging or Computed Tomography scanner. This boundary acts as a skin between points which are determined to be "inside" and "outside" of an object. However, the DMT is vague in regards to exactly where each vertex of the boundary should be placed, which will not necessarily produce smooth results. Mesh smoothing algorithms which ignore the DMT data structures may distort the output mesh so that it could incorrectly include or exclude density points. Thus, an algorithm is presented here which is designed to smooth the output mesh, while obeying the underlying data structures of the DMT algorithm.

The fields of pattern recognition and machine learning are on a fundamental quest to design systems that can learn the way humans do. One important aspect of human intelligence that has so far not been given sufficient attention is the capability of humans to express when they are certain about a decision, or when they are not. Machine learning techniques today are not yet fully equipped to be trusted with this critical task. This work seeks to address this fundamental knowledge gap. Existing approaches that provide a measure of confidence on a prediction such as learning algorithms based on the Bayesian theory or the Probably Approximately Correct theory require strong assumptions or often produce results that are not practical or reliable. The recently developed Conformal Predictions (CP) framework - which is based on the principles of hypothesis testing, transductive inference and algorithmic randomness - provides a game-theoretic approach to the estimation of confidence with several desirable properties such as online calibration and generalizability to all classification and regression methods. This dissertation builds on the CP theory to compute reliable confidence measures that aid decision-making in real-world problems through: (i) Development of a methodology for learning a kernel function (or distance metric) for optimal and accurate conformal predictors; (ii) Validation of the calibration properties of the CP framework when applied to multi-classifier (or multi-regressor) fusion; and (iii) Development of a methodology to extend the CP framework to continuous learning, by using the framework for online active learning. These contributions are validated on four real-world problems from the domains of healthcare and assistive technologies: two classification-based applications (risk prediction in cardiac decision support and multimodal person recognition), and two regression-based applications (head pose estimation and saliency prediction in images). The results obtained show that: (i) multiple kernel learning can effectively increase efficiency in the CP framework; (ii) quantile p-value combination methods provide a viable solution for fusion in the CP framework; and (iii) eigendecomposition of p-value difference matrices can serve as effective measures for online active learning; demonstrating promise and potential in using these contributions in multimedia pattern recognition problems in real-world settings.