We represent arbitrary smooth curved 3D shapes by a discrete set of HOT curves where a surface admits High Order Tangents. These curves determine the structure of the image contours and its catastrophic changes, and there is a natural correspondence between some of them and monocular contour features such as inflections and bitangents. We present a method for automatically constructing the HOT curves from continuous sequences of video images and describe an approach to object recognition using viewpoint-dependent monocular image features as indices into a database of models and as a basis for pose estimation. We have implemented both the methods and present results obtained from real images.