Scale is a fundamental concept in computer vision and pattern recognition, especially in the fields of shape analysis, image segmentation, and registration. It represents the level of detail of object information in scenes. Global scale methods in image processing process the scene at each of various fixed scales and combine the results, as in scale space approaches. Local scale approaches define the largest homogeneous region at each point, and treat these as fundamental units. A similar dichotomy exists for describing shapes also. To vary the level of detail depending on application, it is desirable to be able to detect dominant points on shape boundaries at different scales. In this paper, we compare global and local scale approaches to shape analysis. For global scale, the Curvature Scale Space (CSS) method is selected, which is a state of the art shape descriptor, and is used in the MPEG-7 standard. The local scale approach is based on the notion of curvature-scale (c-scale), which is a new local scale concept that brings the idea of local morphometric scale (such as ball-, tensor-, and generalized scale) developed for images to the realm of boundaries. All previous methods of extracting dominant points lack this concept of a local scale. In this paper, we present a thorough evaluation of these global and local scale methods. Our analysis indicates that locally adaptive scale has advantages over global scale in shape description, just as it has also been demonstrated in image filtering, segmentation, and registration.