The receiver operating characteristic (ROC) curves is a popular tool for evaluating continuous diagnostic tests. The traditional definition of ROC curves incorporates implicitly the idea of "hard" thresholding, which also results in the empirical curves being step functions. The first topic is to introduce a novel definition of soft ROC curves, which incorporates the idea of "soft" thresholding. The softness of a soft ROC curve is controlled by a regularization parameter that can be selected suitably by a cross-validation procedure. A byproduct of the soft ROC curves is that the corresponding empirical curves are smooth. The second topic is on combination of several diagnostic tests to achieve better diagnostic accuracy. We consider the optimal linear combination that maximizes the area under the receiver operating characteristic curve (AUC); the estimates of the combination's coefficients can be obtained via a non-parametric procedure. However, for estimating the AUC associated with the estimated coefficients, the apparent estimation by re-substitution is too optimistic. To adjust for the upward bias, several methods are proposed. Among them the cross-validation approach is especially advocated, and an approximated cross-validation is developed to reduce the computational cost. Furthermore, these proposed methods can be applied for variable selection to select important diagnostic tests. However, the above best-subset variable selection method is not practical when the number of diagnostic tests is large. The third topic is to further develop a LASSO-type procedure for variable selection. To solve the non-convex maximization problem in the proposed procedure, an efficient algorithm is developed based on soft ROC curves, difference convex programming, and coordinate descent algorithm.

This thesis proposes a novel approach to extracting pose information from image sequences. Current state of the art techniques focus exclusively on the image space occupied by the body for pose and action recognition. The method proposed here, however, focuses on the negative spaces: the areas surrounding the individual. This has resulted in the colour-coded negative space approach, an image preprocessing step that circumvents the need for complicated model fitting or template matching methods. The approach can be described as follows: negative spaces surrounding the human silhouette are extracted using horizontal and vertical scanning processes. These negative space areas are more numerous, and undergo more radical changes in shape than the single area occupied by the figure of the person performing an action. The colour-coded negative space representation is formed using the four binary images produced by the scanning processes. Features are then extracted from the colour-coded images. These are based on the percentage of area occupied by distinct coloured regions as well as the bounding box proportions. Pose clusters are identified using feedback from an independent action set. Subsequent images are classified using a simple Euclidean distance measure. An image sequence is thus temporally segmented into its corresponding pose representations. Action recognition simply becomes the detection of a temporally ordered sequence of poses that characterises the action. The method is purely vision-based, utilising monocular images with no need for body markers or special clothing. Two datasets were constructed using several actors performing different poses and actions. Some of these actions included actors waving their arms, sitting down or kicking a leg. These actions were recorded against a monochrome background to simplify the segmentation of the actors from the background. The actions were then recorded on DV cam and digitised into a data base. The silhouette images from these actions were isolated and placed in a frame or bounding box. The next step was to highlight the negative spaces using a directional scanning method. This scanning method colour-codes the negative spaces of each action. What became immediately apparent is that very distinctive colour patterns formed for different actions. To emphasise the action, different colours were allocated to negative spaces surrounding the image. For example, the space between the legs of an actor standing in a T - pose with legs apart would be allocated yellow, while the space below the arms were allocated different shades of green. The space surrounding the head would be different shades of purple. During an action when the actor moves one leg up in a kicking fashion, the yellow colour would increase. Inversely, when the actor closes his legs and puts them together, the yellow colour filling the negative space would decrease substantially. What also became apparent is that these coloured negative spaces are interdependent and that they influence each other during the course of an action. For example, when an actor lifts one of his legs, increasing the yellow-coded negative space, the green space between that leg and the arm decreases. This interrelationship between colours hold true for all poses and actions as presented in this thesis. In terms of pose recognition, it is significant that these colour coded negative spaces and the way the change during an action or a movement are substantial and instantly recognisable. Compare for example, looking at someone lifting an arm as opposed to seeing a vast negative space changing shape. In a controlled research environment, several actors were instructed to perform a number of different actions. After colour coding the negative spaces, it became apparent that every action can be recognised by a unique colour coded pattern. The challenge is to ascribe a numerical presentation, a mathematical quotation, to extract the essence of what is so visually apparent. The essence of pose recognition and it's measurability lies in the relationship between the colours in these negative spaces and how they impact on each other during a pose or an action. The simplest way of measuring this relationship is by calculating the percentage of each colour present during an action. These calculated percentages become the basis of pose and action recognition. By plotting these percentages on a graph confirms that the essence of these different actions and poses can in fact been captured and recognised. Despite variations in these traces caused by time differences, personal appearance and mannerisms, what emerged is a clear recognisable pattern that can be married to an action or different parts of an action. 7 Actors might lift their left leg, some slightly higher than others, some slower than others and these variations in terms of colour percentages would be recorded as a trace, but there would be very specific stages during the action where the traces would correspond, making the action recognisable.In conclusion, using negative space as a tool in human pose and tracking recognition presents an exiting research avenue because it is influenced less by variations such as difference in personal appearance and changes in the angle of observation. This approach is also simplistic and does not rely on complicated models and templates