3 : Scale Invariant Structure Extraction
In the introduction part, we have emphasized the importance of incorporating
graph structure representation with shape analysis. It is normal to construct
a graph structure from morphological shape decomposition. We can simply
treat each part as a node in the graph and the edge relationship is deduced
from the adjacency between each pair of parts. If two parts are adjacent or
overlap then the weight between the two corresponding nodes are non-zero.
In this paper, we dilate the parts with the disk radius size two more than
the origin eroded skeleton. For example, if two parts I and J’s radius are ri
and rj with I and J the corresponding loci, we first dilate these two parts
by the radius ri + 2 and rj + 2. Then the weight between parts I and J is
and(I ⊕ (ri + 2), J ⊕ (rj + 2))/or(I ⊕ (ri + 2), J ⊕ (rj + 2)) which reflect
both the overlap and adjacent relationship. We can use a five nodes graph
to represent the rectangular shape 2 while the center is connected with four
corners.
However, the graph structure constructed from this morphological based
shape decomposition method is not suitable for graph based shape analysis.
It is sensitive to scaling, rotation and noise [7]. An example is shown in Figure
3 here we decompose a set of different size rectangular, we can observe two
things 1) It doesn’t satisfy scale invariant. As we can see, when the scale
is different the decomposition results is different. At the small scale level,
the rectangular shape decomposed skeleton include one line and four small
triangles. While at large scale level, the skeleton include one line and twelve
triangles.
Fig. 2 Graph structure example from morphological shape decomposition.
Fig. 3 Example for the same shape morphological decomposition in different scale.
3.1 Hierarchy Morphological Decomposition
We propose a solution which is to decompose the shape in different scale and
find the corresponding matching parts to represent the shape. The idea is
when a shape is given, we squeeze and enlarge the shape image in a sequence
list. We decompose this sequence image shapes. We then find the corresponding
parts for this sequence shape decomposition. The stable scale invariant
shape decomposition is then found by choose the parts which appear in all
different scale levels.
In Figure 3, we still use the example of the rectangular, we first squeeze
and enlarge the shape by 15 percent each time. We choose three squeezed and
three enlarged shapes – altogether we have five shapes. We then decompose
this sequence through morphological decomposition described in the previous
section. We then find the correspondence in a hierarchy style. From the
correspondence results, we notice that the parts which appear in all levels are
the center line and four dots in the corners. The proposed methods can solve
the scale invariants problem for shape decomposition. Like SIFT feature [5],
we consider the shape decomposition through a hierarchy way.
In the introduction part, we have emphasized the importance of incorporating
graph structure representation with shape analysis. It is normal to construct
a graph structure from morphological shape decomposition. We can simply
treat each part as a node in the graph and the edge relationship is deduced
from the adjacency between each pair of parts. If two parts are adjacent or
overlap then the weight between the two corresponding nodes are non-zero.
In this paper, we dilate the parts with the disk radius size two more than
the origin eroded skeleton. For example, if two parts I and J’s radius are ri
and rj with I and J the corresponding loci, we first dilate these two parts
by the radius ri + 2 and rj + 2. Then the weight between parts I and J is
and(I ⊕ (ri + 2), J ⊕ (rj + 2))/or(I ⊕ (ri + 2), J ⊕ (rj + 2)) which reflect
both the overlap and adjacent relationship. We can use a five nodes graph
to represent the rectangular shape 2 while the center is connected with four
corners.
However, the graph structure constructed from this morphological based
shape decomposition method is not suitable for graph based shape analysis.
It is sensitive to scaling, rotation and noise [7]. An example is shown in Figure
3 here we decompose a set of different size rectangular, we can observe two
things 1) It doesn’t satisfy scale invariant. As we can see, when the scale
is different the decomposition results is different. At the small scale level,
the rectangular shape decomposed skeleton include one line and four small
triangles. While at large scale level, the skeleton include one line and twelve
triangles.
Fig. 2 Graph structure example from morphological shape decomposition.
Fig. 3 Example for the same shape morphological decomposition in different scale.
3.1 Hierarchy Morphological Decomposition
We propose a solution which is to decompose the shape in different scale and
find the corresponding matching parts to represent the shape. The idea is
when a shape is given, we squeeze and enlarge the shape image in a sequence
list. We decompose this sequence image shapes. We then find the corresponding
parts for this sequence shape decomposition. The stable scale invariant
shape decomposition is then found by choose the parts which appear in all
different scale levels.
In Figure 3, we still use the example of the rectangular, we first squeeze
and enlarge the shape by 15 percent each time. We choose three squeezed and
three enlarged shapes – altogether we have five shapes. We then decompose
this sequence through morphological decomposition described in the previous
section. We then find the correspondence in a hierarchy style. From the
correspondence results, we notice that the parts which appear in all levels are
the center line and four dots in the corners. The proposed methods can solve
the scale invariants problem for shape decomposition. Like SIFT feature [5],
we consider the shape decomposition through a hierarchy way.
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