Object detection is a fundamental task in computer vision which serves many important problems such as image segmentation and object tracking. Current major application areas include medical image interpretation, remote sensing, video image analysis, and surveillance. Many studies have focused on variational formulations because they result in the most effective algorithms. By minimizing a functional which can easily encode various segmentation constraints, variational formulations have offered a convenient framework to develop accurate and efficient algorithms. In this talk, we present some variational techniques we proposed using active contours and graph cuts for image segmentation and object tracking.