Speaker
Description
In archaeology it is a common task to extract incisions or glyphs from a surface. This procedure is usually done manually and, therefore, it is prone to errors and it can be extremely time consuming. In this talk we present a variational model to automatically extract these incisions from a smooth surface.
We model this problem in the following way. Let $\mathbf{x}\in\mathbb{R}^n$ be a vector containing a sampling of the archaeological surface, we wish to find two vectors $\mathbf{x}_s^*$ and $\mathbf{x}_g^*$ such that $\mathbf{x}=\mathbf{x}_s^*+\mathbf{x}_g^*$, where $\mathbf{x}_s^*$ is smooth and contains the background and $\mathbf{x}_g^*$ is sparse and contains the glyph. To this aim we consider the model
$$
\begin{split}
\left(\mathbf{x}_s^*,\mathbf{x}_g^*\right)=&\arg\min_{\mathbf{x}_s,\mathbf{x}_g\in\mathbb{R}^{n\times n}} \frac{1}{2}\left\|L^\alpha\textbf{x}_s\right\|_2^2+\mu\left\|\mathbf{x}_g\right\|_1,\\&\quad \mbox{s.t. }\mathbf{x}_s+\mathbf{x}_g=\mathbf{x},
\end{split}
$$
where $\mu>0$, $\alpha\in[1,2]$, $$\|\mathbf{x}\|_p^p=\sum_{i=1}^{n}|\mathbf{x}_i|^p,$$ and $L\in\mathbb{R}^{n\times n}$ denotes the Laplacian operator. To perform the minimization,
we employ the Alternating Direction Multiplier Method (ADMM). We provide a procedure to generate
realistic synthetic data and we show the performances of the proposed method on this kind of data.
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