A visual representation model is an abstract pattern used to create images which characterize quantitative information. By using a texture image to define a visual representation model, correspondence of color to denote similarity, and correspondence of image location over multiple images to associate information into collections, highly effective visualization techniques are made possible. One such technique for two-dimensional texture-based vector field visualization is vector field marquetry. Vector
field marquetry uses a synthesized image representing direction as a conditioner for pixel replacement over a collection of vector field direction-magnitude portraits. The resulting synthesized image displays easily recognizable local and global features, vector direction, and magnitude. A related technique enabled by correspondence-based methods is the sparse representation of a vector field by a topological skeleton constructed from isodirection lines. Each vector in a vector field along an isodirection line points in the same direction. Isodirection lines subdivide the domain into regions of similar vectors, converge at critical points,
and represent global characteristics of the vector field.
Texture-based correspondence display is a methodology to display corresponding data elements in visual representations of complex multidimensional, multivariate data. A visual representation model is the abstract pattern used to transform numerical data to an image. It is challenging to develop visual representation models for multidimensional, multivariate data that are at once a comprehensive representation of the data and visually simple enough as to avoid confusion. Using multiple images increases the degrees of freedom of data representation with color or location serving as a means to show correspondence of the information among the images. The correspondence display techniques described utilize texture as a persistent medium to contain a visual representation model and as a means to create multiple renditions of data where color is used to identify correspondence. These techniques allow corresponding data elements to be displayed over a variety of visual metaphors in a normal rendering process without the addition of extraneous linking metadata creation and maintenance. Texture-based correspondence display extends the effectiveness of visual representation for understanding data to the understanding and creation of visual representation models.