Abstract: Fisher Linear Discriminant Analysis (FLDA) is one of the most popular techniques used in classification applying dimensional reduction. The numerical scheme involves the inversion of the within-class scatter matrix, which makes FLDA potentially ill-conditioned when it becomes singular. In this paper we present a novel explicit formulation of FLDA in terms of the eccentricity ratio and eigenvector orientations of the within-class scatter matrix. An analysis of this function will characterize those situations where FLDA response is not reliable because of numerical instability. This can solve common situations of poor classification performance in computer vision.

Abstract: Videobronchoscopy is a medical imaging technique that allows interactive navigation inside the respiratory pathways. This imaging modality provides realistic images and allows non-invasive minimal intervention procedures. Tracheal procedures are routinary interventions that require assessment of the percentage of obstructed pathway for injury (stenosis) detection. Visual assessment in videobronchoscopic sequences requires high expertise of trachea anatomy and is prone to human error.
This paper introduces an automatic method for the estimation of steneosed trachea percentage reduction in videobronchoscopic images. We look for tracheal rings , whose deformation determines the degree of obstruction. For ring extraction , we present a ring detector based on an illumination and appearance model. This model allows us to parametrise the ring detection. Finally, we can infer optimal estimation parameters for any video resolution.

Abstract: Empirical and mechanistic models differ in their approaches to the analysis of pharmacological effect. Whereas the parameters of the former are not physical constants those of the latter embody the nature, often complex, of biology. Empirical models are exclusively used for curve fitting, merely to characterize the shape of the E/[A] curves. Mechanistic models, on the contrary, enable the examination of mechanistic hypotheses by parameter simulation. Regretfully, the many parameters that mechanistic models may include can represent a great difficulty for curve fitting, representing, thus, a challenge for computational method development. In the present study some empirical and mechanistic models are shown and the connections, which may appear in a number of cases between them, are analyzed from the curves they yield. It may be concluded that systematic and careful curve shape analysis can be extremely useful for the understanding of receptor function, ligand classification and drug discovery, thus providing a common language for the communication between pharmacologists and medicinal chemists.

Abstract: Recent advances in endoscopic devices have increased their use for minimal invasive diagnostic and intervention procedures. Among all endoscopic modalities, bronchoscopy is one of the most frequent with around 261 millions of procedures per year. Although the use of bronchoscopy is spread among clinical facilities it presents some drawbacks, being the visual inspection for the assessment of anatomical measurements the most prevalent of them. In
particular, inaccuracies in the estimation of the degree of stenosis (the percentage of obstructed airway) decreases its diagnostic yield and might lead to erroneous treatments. An objective computation of tracheal stenosis in bronchoscopy videos would constitute a breakthrough for this non-invasive technique and a reduction in treatment cost.
This thesis settles the first steps towards on-line reliable extraction of anatomical information from videobronchoscopy for computation of objective measures. In particular, we focus on the computation of the degree of stenosis, which is obtained by comparing the area delimited by a healthy tracheal ring and the stenosed lumen. Reliable extraction of airway structures in interventional videobronchoscopy is a challenging task. This is mainly due to the large variety of acquisition conditions (positions and illumination), devices (different digitalizations) and in videos acquired at the operating room the unpredicted presence of surgical devices (such as probe ends). This thesis contributes to on-line stenosis assessment in several ways. We
propose a parametric strategy for the extraction of lumen and tracheal rings regions based on the characterization of their geometry and appearance that guide a deformable model. The geometric and appearance characterization is based on a physical model describing the way bronchoscopy images are obtained and includes local and global descriptions. In order to ensure a systematic applicability we present a statistical framework to select the optimal
parameters of our method. Experiments perform on the first public annotated database, show that the performance of our method is comparable to the one provided by clinicians and its computation time allows for a on-line implementation in the operating room.

Abstract: Optical Flow (OF) is the input of a wide range of decision support systems such as car driver assistance, UAV guiding or medical diagnose. In these real situations, the absence of ground truth forces to assess OF quality using quantities computed from either sequences or the computed optical flow itself. These quantities are generally known as Confidence Measures, CM. Even if we have a proper confidence measure we still need a way to evaluate its ability to discard pixels with an OF prone to have a large error. Current approaches only provide a descriptive evaluation of the CM performance but such approaches are not capable to fairly compare different confidence measures and optical flow algorithms. Thus, it is of prime importance to define a framework and a general road map for the evaluation of optical flow performance.
This thesis provides a framework able to decide which pairs “ optical flow – confidence measure” (OF-CM) are best suited for optical flow error bounding given a confidence level determined by a decision support system. To design this framework we cover the following points:
Descriptive scores. As a first step, we summarize and analyze the sources of inaccuracies in the output of optical flow algorithms. Second, we present several descriptive plots that visually assess CM capabilities for OF error bounding. In addition to the descriptive plots, given a plot representing OF-CM capabilities to bound the error, we provide a numeric score that categorizes the plot according to its decreasing profile, that is, a score assessing CM performance.
Statistical framework. We provide a comparison framework that assesses the best suited OF-CM pair for error bounding that uses a two stage cascade process. First of all we assess the predictive value of the confidence measures by means of a descriptive plot. Then, for a sample of descriptive plots computed over training frames, we obtain a generic curve that will be used for sequences with no ground truth. As a second step, we evaluate the obtained general curve and its capabilities to really reflect the predictive value of a confidence measure using the variability across train frames by means of ANOVA.
The presented framework has shown its potential in the application on clinical decision support systems. In particular, we have analyzed the impact of the different image artifacts such as noise and decay to the output of optical flow in a cardiac diagnose system and we have improved the navigation inside the bronchial tree on bronchoscopy.