Image Processing Reference

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(27)

where ∅
prod
(
x
,
y
) =∅ (
x
,
y
) · ∅
ref
(
x
,
y
), ∅ is the level set function associated to the evolving

contour, while∅
ref
is the level set function associated to the shape of reference after alignment.

As it can be seen, the new proposed stopping function only allows for updating the level set

function in the regions of variability between shapes. In these regions,
g
shape
is either 1 or − 1

because in the case of partial occlusions, the function is equal to 1 in order to push the edge

inward (deflate) and in case of missing parts, this function is equal to − 1 to push the contour

toward the outside (inflate). This property recalls the Balloon snake's model proposed by Co-

ginning. In our work, the direction of evolution is handled automatically based on the sign of

∅
ref
. The total discrete evolution's equation that we propose is as follows:

(28)

w
is a weighting factor between the image-based force and knowledge-driven force. See Ref.

4 Experimental results

4.1 Robustness of the Proposed Shape Priors

We present in
Figure 5
an example of successive evolutions between several shapes of diferent

topologies under the proposed shape priors only (
w
= 0). By the first row, the initial shape is a

simple square while the target is a tree leaf. For the second row, the final shape obtained after

several iterations in the first row is used as initial contour. The template in this case consists of

two contours. This experiment proves that the proposed shape constraint can act on the topo-

logy of the original curve. Finally, by the third row, we show the ability of our shape prior to

detect objects with holes.

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