In this dissertation, we focus on solving Nonlinear Least Squares problems using a supervised approach. In particular, we developed a Supervised Descent Method (SDM), performed thorough theoretical analysis, and demonstrated its effectiveness on optimizing analytic functions, and four other real-world applications: Inverse Kinematics, Rigid Tracking, Face Alignment (frontal and multi-view), and 3D Object Pose Estimation. In Rigid Tracking, SDM was able to take advantage of more robust features, such as, HoG and SIFT. Those non-differentiable image features were out of consideration of previous work because they relied on gradient-based methods for optimization. In Inverse Kinematics where we minimize a non-convex function, SDM achieved significantly better convergence than gradient-based approaches. In Face Alignment, SDM achieved state-of-the-arts results. Moreover, it was extremely computationally efficient, which makes it applicable for many mobile applications. In addition, we provided a unified view of several popular methods including SDM on sequential prediction, and reformulated them as a sequence of function compositions. Finally, we suggested some future research directions on SDM and sequential prediction.

Modern facial feature tracking techniques can automatically extract and accurately track multiple facial landmark points from faces in video streams in real time. Facial landmark points are defined as points distributed on a face in regards to certain facial features, such as eye corners and face contour. This opens up for using facial feature movements as a handsfree human-computer interaction technique. These alternatives to traditional input devices can give a more interesting gaming experience. They also open up for more intuitive controls and can possibly give greater access to computers and video game consoles for certain disabled users with difficulties using their arms and/or fingers. This research explores using facial feature tracking to control a character's movements in a platform game. The aim is to interpret facial feature tracker data and convert facial feature movements to game input controls. The facial feature input is compared with other handsfree inputmethods, as well as traditional keyboard input. The other handsfree input methods that are explored are head pose estimation and a hybrid between the facial feature and head pose estimation input. Head pose estimation is a method where the application is extracting the angles in which the user's head is tilted. The hybrid input method utilises both head pose estimation and facial feature tracking. The input methods are evaluated by user performance and subjective ratings from voluntary participants playing a platform game using the input methods. Performance is measured by the time, the amount of jumps and the amount of turns it takes for a user to complete a platform level. Jumping is an essential part of platform games. To reach the goal, the player has to jump between platforms. An inefficient input method might make this a difficult task. Turning is the action of changing the direction of the player character from facing left to facing right or vice versa. This measurement is intended to pick up difficulties in controling the character's movements. If the player makes many turns, it is an indication that it is difficult to use the input method to control the character movements efficiently. The results suggest that keyboard input is the most effective input method, while it is also the least entertaining of the input methods. There is no significant difference in performance between facial feature input and head pose input. The hybrid input version has the best results overall of the alternative input methods. The hybrid input method got significantly better performance results than the head pose input and facial feature input methods, while it got results that were of no statistically significant difference from the keyboard input method. Keywords: Computer Vision, Facial Feature Tracking, Head Pose Tracking, Game Control / Moderna tekniker kan automatiskt extrahera och korrekt följa multipla landmärken från ansikten i videoströmmar. Landmärken från ansikten är definerat som punkter placerade på ansiktet utefter ansiktsdrag som till exempel ögat eller ansikts konturer. Detta öppnar upp för att använda ansiktsdragsrörelser som en teknik för handsfree människa-datorinteraktion. Dessa alternativ till traditionella tangentbord och spelkontroller kan användas för att göra datorer och spelkonsoler mer tillgängliga för vissa rörelsehindrade användare. Detta examensarbete utforskar användbarheten av ansiktsdragsföljning för att kontrollera en karaktär i ett plattformsspel. Målet är att tolka data från en appliktion som följer ansiktsdrag och översätta ansiktsdragens rörelser till handkontrollsinmatning. Ansiktsdragsinmatningen jämförs med inmatning med huvudposeuppskattning, en hybrid mellan ansikstdragsföljning och huvudposeuppskattning, samt traditionella tangentbordskontroller. Huvudposeuppskattning är en teknik där applikationen extraherar de vinklar användarens huvud lutar. Hybridmetoden använder både ansiktsdragsföljning och huvudposeuppskattning. Inmatningsmetoderna granskas genom att mäta effektivitet i form av tid, antal hopp och antal vändningar samt subjektiva värderingar av frivilliga testanvändare som spelar ett plattformspel med de olika inmatningsmetoderna. Att hoppa är viktigt i ett plattformsspel. För att nå målet, måste spelaren hoppa mellan plattformar. En inefektiv inmatningsmetod kan göra detta svårt. En vändning är när spelarkaraktären byter riktning från att rikta sig åt höger till att rikta sig åt vänster och vice versa. Ett högt antal vändningar kan tyda på att det är svårt att kontrollera spelarkaraktärens rörelser på ett effektivt sätt. Resultaten tyder på att tangentbordsinmatning är den mest effektiva metoden för att kontrollera plattformsspel. Samtidigt fick metoden lägst resultat gällande hur roligt användaren hade under spelets gång. Där var ingen statisktiskt signifikant skillnad mellan huvudposeinmatning och ansikstsdragsinmatning. Hybriden mellan ansiktsdragsinmatning och huvudposeinmatning fick bäst helhetsresultat av de alternativa inmatningsmetoderna. Nyckelord: Datorseende, Följning av Ansiktsdrag, Följning av Huvud, Spelinmatning

In this study a fully automatic and scale invariant feature extractor which does not require manual initialization or special equipment is proposed. Face location and size is extracted using skin segmentation and ellipse fitting. Extracted face region is scaled to a predefined size, later upper and lower facial templates are used for feature extraction. Template localization and template parameter calculations are carried out using Principal Component Analysis. Changes in facial feature coordinates between analyzed image and neutral expression image are used for expression classification. Performances of different classifiers are evaluated. Performance of proposed feature extractor is also tested on sample video sequences. Facial features are extracted in the first frame and KLT tracker is used for tracking the extracted features. Lost features are detected using face geometry rules and they are relocated using feature extractor. As an alternative to feature based technique an available holistic method which analyses face without partitioning is implemented. Face images are filtered using Gabor filters tuned to different scales and orientations. Filtered images are combined to form Gabor jets. Dimensionality of Gabor jets is decreased using Principal Component Analysis. Performances of different classifiers on low dimensional Gabor jets are compared. Feature based and holistic classifier performances are compared using JAFFE and AF facial expression databases.