| dc.description.abstract | The theory of multi-view geometry concerns the reconstruction of a landscape from multiple images. We will analyze the reconstruction of \(\P^2\) from \(n\) images, for \(n=2,3,4\). A reconstruction of \(\P^2\) consists of finding a surface \(S\subseteq (\P^1)^n\) and a birational map \(\alpha\) from \(S\) back to \(\P^2\), when \(S\) is embedded into \(\P^{2^n-1}\) using the Segre embedding. When \(n=2\), then \(S=(\P^1)^2\) and \(\alpha\) is a projection from a specific point \(q\) on \(S\) in \(\P^3\). When \(n=3\) and \(n=4\), then \(S\subset(\P^1)^n\), and \(\alpha\) is a projection from the span \(\langle C\rangle\), restricted to \(S\), where \(C\) is a curve in \(S\) in \(\P^{2^n-1}\). As we will see, when the number of images used to reconstruct \(\P^2\) increases, there is less ambiguity in the reconstruction. We will analyze the ambiguity for \(n=2,3,4\) images. | eng |