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                <editor>Cris L. Luengo Hendriks</editor>
                <editor>Gunilla Borgefors</editor>
                <editor>and Robin Strand</editor>
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              <p>In this paper we present a reconstruction method controlled by the evolution of attributes. The process begins from a marker, propagated over increasing quasi-flat zones. The evolution of several increasing and non-increasing attributes is studied in order to select the appropriate region. Additionally, the combination of attributes can be used in a straightforward way. To demonstrate the performance of our method, three applications are presented. Firstly, our method successfully segments connected objects in range images. Secondly, input-adaptive structuring elements (SE) are defined computing the controlled propagation for each pixel on a pilot image. Finally, input-adaptive SE are used to assess shape features on the image. Our approach is multi-scale and auto-dual. Compared with other methods, it is based on a given attribute but does not require a size parameter in order to determine appropriate regions. It is useful to extract objects of a given shape. Additionally, our reconstruction is a connected operator since quasi-flat zones do not create new contours on the image.</p>
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