We address the problem of tracking points in dense vector fields. Such vector fields may come from computational fluid dynamics simulations, environmental monitoring sensors, or dense point tracking of video data. To track points in vector fields, we capture the distribution of higher-order properties (e.g., properties derived from the gradient of the velocity vector field) in a novel local descriptor called a vector spin-image. Our distribution-based approach has a number of advantages over methods that use topology analysis to track points in vector fields. The local distributions are robust to noise, adaptable to changes in the feature, and can be used to extrapolate the location of features after they have disappeared. We describe the vector spin-image data structure, the higher-order properties we record to track vector field points, and show results of tracking points in the simulated flow through a diesel engine cylinder.

Vector fields may come from video data (via optical flow and tracking), from weather phenomena (e.g., wind speed and direction), and from medical imaging. An important component in analyzing this data is to be able to quantitatively compare different points within a vector field or across different fields of the same type. We present a novel local descriptor to compare individual points in a vector field and rank them based on which are most similar to a selected point. The descriptor captures the statistics of the neighboring vector field around a central point and is discriminating, robust to noise, and efficient to generate and compare.

Johnson and Hebert’s spin-images have been applied to the registration of range images and object recognition with much success because they are rotation, scale, and pose invariant. In this paper we address two issues concerning spin-images, namely: (1) comparing uncompressed spinimages across large datasets is costly, and (2) a method to select the appropriate bin size and image width for spinimages is not clearly defined. Our solution to these issues is a multi-resolution method that generates a pyramid of spin-images by successively decreasing the spin-image size by powers of two. To efficiently correlate surface points, we compare spin-images in a low-to-high resolution manner. Once multi-resolution spin-images are generated for a given object, we have found that the different resolutions can also be used to compare objects that have differing or non-uniform point densities. To select the appropriate bin sizes for comparing such objects, we use the ratio of the average edge lengths of the objects. We also show preliminary results of using the pyramid to converge on the appropriate image width by traversing the pyramid in a low-to-high resolution manner looking for the highest resolution at which the fewest number of highly correlated points are found to match a given feature point.