This paper addresses the problem of recognizing three-dimensional objects bounded by smooth curved surfaces from image contours found in a single photograph. The proposed approach is based on a viewpoint-invariant relationship between object geometry and certain image features under weak perspective projection. The image features themselves are viewpoint-dependent. Concretely, the set of all possible silhouette bitangents, along with the contour points sharing the same tangent direction, is the projection of a one-dimensional set of surface points where each point lies on the occluding contour for a five-parameter family of viewpoints. These image features form a one-parameter family of equivalence classes, and it is shown that each class can be characterized by a set of numerical attributes that remain constant across the corresponding five-dimensional set of viewpoints. This is the basis for describing objects by “invariant” curves embedded in high-dimensional spaces. Modeling is achieved by moving an object in front of a camera and does not require knowing the object-to-camera transformation; nor does it involve implicit or explicit three-dimensional shape reconstruction. At recognition time, attributes computed from a single image are used to index the model database, and both qualitative and quantitative verification procedures eliminate potential false matches. The approach has been implemented and examples are presented.

: 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. 1 Introduction While implemented recognition systems based on parametric shape representations such as algebraic surfaces or superquadrics have demonstrated their usefulness, the ultimate utility of a representation is limited by its scope. This suggests looking for a more general representation ...

The silhouette of a smooth 3D object observed by a moving camera changes over time. Past work has shown how surface geometry can be recovered using the deformation of the silhouette when the camera motion is known. This paper addresses the problem of estimating both the full Euclidean surface structure and the camera motion from a dense set of silhouettes captured under orthographic or scaled orthographic projection. The approach relies on a viewpoint-invariant representation of curves swept by viewpoint-dependent features such as bitangents, inflections and contour points with parallel tangents. Feature points, which form stereo frontier points between non-consecutive images, are matched using this representation. The camera's angular velocity is computed from constraints derived from this correspondence along with the image velocity of these features. From the angular velocity, the epipolar geometry is ascertained, and infinitesimal motion frontier points can be detected. In turn, the motion of these frontier points constrains the translation component of camera motion. Finally, the surface is reconstructed using established techniques once the camera motion has been estimated.

To recognize three-dimensional objects bounded by smooth curved surfaces from monocular image contours, viewpoint-dependent image features must be related to object geometry. Contour bitangents and inflections along with associated parallel tangents points are the projection of surface points that lie on the occluding contour for a five-parameter family of scaled orthographic projection viewpoints. An invariant representation can be computed from these image features and seen for modeling and recognizing objects. Modeling is achieved by moving an object in front of a camera to obtain a curve of possible invariants. The relative camera-object motion is not required, and 3D models are not utilized. At recognition time, invariants computed from a single image are used to index the model database. Using the matched features, independent qualitative and quantitative verification procedures eliminate potential false matches. Examples from an implementation are presented.>

Arbitrary smooth curved 3D shapes are represented by a discrete set of high-order tangent (HOT) curves, where a surface admits HOTs. 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 of the methods, and present results obtained from real images.>

An approach is presented for reconstructing two types of 3-D higher order tangency (HOT) curves from a sequence of images. These curves are useful for object recognition. The reconstruction results for bitangents are encouraging in comparison to those of inflections. They are probably more accurately reconstructed because they are readily located in images, and their common tangent is very accurately estimated from the point locations. This makes bitangents a good feature choice for recognition.>