Content-based indexing of images and video

Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

The knowledge used in vision and where it comes from

Knowledge is often thought to be something brought from outside to act upon the visual messages received from the eye in a 'top-down' fashion, but this is a misleadingly narrow view. First, the visual system is a multilevel heterarchy with connections acting in all directions so it has no 'top'; and second, knowledge is provided through innately determined structure and by analysis of the redundancy in sensory messages themselves, as well as from outside. This paper gives evidence about mechanisms analysing sensory redundancy in biological vision. Automatic gain controls for luminance and contrast depend upon feedback from the input, and there are strong indications that the autocorrelation function, and other associations between input variables, affect the contrast sensitivity function and our subjective experience of the world. The associative structure of sensory message can provide much knowledge about the world we live in, and neural mechanisms that discount established associative structure in the input messages by recoding them can improve survival by making new structure more easily detectable. These mechanisms may be responsible for illusions, such as those produced by a concave face-mask, that are classically attributed to top-down influences.