Image Processing Reference

In-Depth Information

Table 2

The Estimated Affine Motion Parameters

l
0

α

A

Shapes of (b) 0.002 1.003

Shapes of (d) 0

2.004

2.3 Discussion

Having the parameters of the affine or Euclidean transformations between the two contours,

we perform the alignment of the two curves to determine the regions of variability between

shapes by computing the product function of the signed distance functions associated to level

set functions of, respectively, the target and the reference object after alignment given by

(19)

where and
f
∅
are the two binary images associated, respectively, to ∅
ref
and ∅. See Ref.

variability between the two binary images and
f
∅
due to occlusion, cluter, or missing

parts, whereas in positive regions, the objects are similar. Thus, in what follows, we propose

to update the level set function ∅, only in regions of variability between shapes to make the

evolving contours overpass the spurious edges and recover the desired shapes of objects. This

property recalls the narrow band technique used to accelerate the evolution of the level set

2.4 Global Matching Using Affine Invariants Descriptors

In presence of many templates, we have to choose the most suitable one according to the

evolving curve. Let
α
and
β
be positive real numbers, and
k
0
, k
1
, k
2
, and
k
3
four positive integers.

Let
C
n
x
and
C
n
y
be the complex Fourier coefficients of the coordinates (
u
,
v
). Δ denotes the

determinant.

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