05904854

a

05904854 Naegel, Beno\^\i t Passat, Nicolas Ronse, Christian 3D angiographic image segmentation. Najman, Laurent (ed.) et al., Mathematical morphology. From theory to applications. London: ISTE; Hoboken, NJ: John Wiley \& Sons (ISBN 978-1-84821-215-2/hbk). 375-383 (2010). 2010 London: ISTE; Hoboken, NJ: John Wiley \& Sons EN image segmentation image morphology Two types of image segmentation models are advocated. The first, termed {\it{anatomical knowledge modeling}}, advocates creating shape models that describe general shapes of objects of interest. As an example, the authors define $\Cal{M}: E\to [0,1]$, where $E$ is the space on which the structure of interest is defined and $\Cal{M}(x)$ denotes the mean presence ratio of the structure at point $x$. A second approach uses simpler morphological hypotheses, estimating the values of certain parameters according to position within an image. A typical model has the form, $\Cal{A}: E\to [0,1]\times \Cal{P}[0,\infty)\times\Cal{P} [0,\pi)^2$ with $(\Cal{A}^d(x), \Cal{A}^t(x), \Cal A^o(x))$ representing fields related to presence probability, size, and orientation, respectively. The {\it{hit-or-miss}} transform is discussed in this context, defined as composition $V\circ D_{A,B}$ of a fitting operator $D_{A,B}:\Bbb{Z}^E\to \Cal{P}(E\times \Bbb{Z})$ with $I\in \Bbb{Z}^E$ mapping to $\{(p,t)\in E\times\Bbb{Z}: A_{p,t}\leq I\leq B_{p,t}\}$ and the valuation operator $V:\Cal{P}(E\times\Bbb{Z})\to \Bbb{Z}^E$ with $\leq$ denoting pointwise inequality of functions and $A,B:E\to\Bbb{Z}$ denoting structuring functions. Two concrete examples are provided, one involving liver vascular network segmentation from X-ray CT-scans and the second involving brain vessel segmentation from MRI data. In each case, the models outlined above are described in more explicit terms. Joseph Lakey (Las Cruces)