  We introduce a new formalism and a number of new results in the context of
geometric computational vision. The classical scope of the research in
geometric computer vision is essentially limited to static configurations of
points and lines in $P^3$ . By using some well known material from algebraic
geometry, we open new branches to computational vision. We introduce algebraic
curves embedded in $P^3$ as the building blocks from which the tensor of a
couple of cameras (projections) can be computed. In the process we address
dimensional issues and as a result establish the minimal number of algebraic
curves required for the tensor variety to be discrete as a function of their
degree and genus. We then establish new results on the reconstruction of an
algebraic curves in $P^3$ from multiple projections on projective planes
embedded in $P^3$ . We address three different presentations of the curve: (i)
definition by a set of equations, for which we show that for a generic
configuration, two projections of a curve of degree d defines a curve in $P^3$
with two irreducible components, one of degree d and the other of degree $d(d -
1)$, (ii) the dual presentation in the dual space $P^{3*}$, for which we derive
a lower bound for the number of projections necessary for linear reconstruction
as a function of the degree and the genus, and (iii) the presentation as an
hypersurface of $P^5$, defined by the set of lines in $P^3$ meeting the curve,
for which we also derive lower bounds for the number of projections necessary
for linear reconstruction as a function of the degree (of the curve). Moreover
we show that the latter representation yields a new and efficient algorithm for
dealing with mixed configurations of static and moving points in $P^3$.
