Exploiting geometric and spatial constraints for vision and lighting applications

Geometric constraints and spatial constraints are ubiquitous in the physical world we live in. Some simple examples are: Contours of human organs are usually smooth; Knee cartilages always grow on specific areas of knee bone surfaces; Light travels in straight lines in homogeneous media. Many of these constraints are very intuitive and easy to explain. In computer vision and pattern recognition problems, a popular approach to improve the performance of a model is to add such geometric and spatial constraints into the mathematical model. However, although most constraints are very intuitive, incorporating such constraints into a mathematical model is usually difficult. Geometric and spatial constraints often either have no straightforward mathematical formulation, or have formulations that are too difficult to solve with the model.;In this thesis, we propose three original methods for computer vision and smart lighting applications: the Active Geometric Shape Model (AGSM) method, the Semantic Context Forests method, and the Color-Sensor-Based Occupancy Sensing (COSBOS) method. In all these methods, we exploit either geometric constraints or spatial constraints that are intuitive in the corresponding problems.;The active geometric shape model is a method to fit a geometric shape to 2D images. A simple example problem is to fit an ellipse to an image efficiently. Unlike the popular Hough transform method, which is based on an exhaustive search in the parameter space, our active geometric shape model iteratively adjusts shape parameters according to the geometric meaning of each parameter, thus it is very fast and uses little memory. The key idea behind this method is to exploit the geometric constraints of different shape parameters in the image domain. This method is not only validated on synthetic data, but also has a good application in the detection and segmentation of cerebrospinal fluid (CSF) from 2D magnetic resonance (MR) image sequences.;The semantic context forests method segments multiple objects in medical images. This method is proposed to solve the knee cartilage segmentation from 3D MR images problem. The most important spatial constraint in this problem is that knee cartilage grows in only certain areas of the corresponding bone surface. Most existing knee cartilage segmentation methods incorporate such constraints by explicitly extracting a bone-cartilage interface (BCI). Our semantic context forests method is an alternative of BCI-based methods. We exploit such spatial constraints by incorporating them into machine learning algorithms. We developed four new kinds of features: signed distance to bone (SDTB) features, distance to anatomic landmark (DTAL) features, random shift intensity difference (RSID) features, and random shift probability difference (RSPD) features. These four feature sets encode the spatial constraints not only between knee bones and knee cartilages, but also between different knee cartilages. A multi-pass random forests classifier with such features resulted in very good segmentation performance.;The color-sensor-based occupancy sensing method is a novel technique that we developed for smart lighting applications. Unlike traditional vision problems where cameras are used to capture images, we monitor indoor spaces by employing color-controllable LED fixtures and distributed low-cost non-imaging color sensors. To estimate the occupancy distribution in the indoor space, we incorporate the geometric and spatial constraints between the fixtures, the room, and the sensors into our geometrical optics models. The three most important models that we use are the light transport model (LTM), the light blockage model (LBM), and the light reflection model (LRM).;Although these three methods solve problems in different domains, they share a common key idea: incorporate the geometric and spatial constraints in the problem with the mathematical model. These constraints significantly improve the performance of the models in the corresponding applications.