A problem central to visual scene understanding and computer vision is to extract semantically meaningful parts of images. A visual scene consists of objects, and the objects and parts of objects are delineated from their surrounding by closed contours. In this thesis a new bottom-up visual operator, called the Torque operator, which captures the concept of closed contours is introduced. Its computation is inspired by the mechanical definition of torque or moment of force, and applied to image edges. It takes as input edges and computes over regions of different size a measure of how well the edges are aligned to form a closed, convex contour. The torque operator is by definition scale independent, and can be seen as an operator of mid-level vision that captures the organizational concept of 'closure' and grouping mechanism of edges. In this thesis, fundamental properties of the torque measure are studied, and experiments are performed to demonstrate and verify that it can be made a useful tool for a variety of applications, including visual attention, segmentation, and boundary edge detection.