Shape Template Scaling and Rotation

When the user draws the sketch that will be used as a template, it is in an arbitrary scale and, in general, has an unknown relation with the scale of the objects it has to match.

If we cover the image with a coordinate system (x, y), each interesting objects can be identified by its minimum enclosing rectangles (MER), with sides parallel to the coordinate axes and lower left and upper right corners {(x1, y1), (x2, y2)}. We consider the aspect ratio of the rectangle:

p=(y2-y1)/(x2-x1)

The sketch is similarly enclosed in its MER with extrema{(X1,Y1),(X2,Y2)} which has an aspect ratio:

P=(Y2-Y1)/(X2-X1)

We can assume that the user, while making a query, draws an object approximately with the same aspect ratio of the object he wants to retrieve.

  • For this reason, we can mark as nonmatched all those objects in the image whose aspect ratio is not such that:

1/k<P/p<k (where k is a fixed threshold)

  • All the interesting rectangles that pass this sieve are candidates for matching.

To speed up this checking, aspect ratios are organized into a binary tree index structure.

  • Each node of the tree includes pointers to image rectangles with that aspect ratio.
  • Matching is improved

    if we normalize the sizes of both the template in the 

    sketch and the shape in the image.

33

 

In practice, it is almost impossible for the user to reproduce object mutual orientations exactly as they are in the searched image.

To cope with this inherent imprecision of the user query, given an object oi its orientation with respect to oj was evaluated
by considering the position of the oi centroid with respect to the oj boundaries.

In the very general case of sketches composed of multiple templates, a candidate image is retrieved if and only if:
1) it has two—or more—areas of interest in the same spatial relationships as the templates drawn on the screen;
2) the shapes contained in the areas of interest match the templates of the sketch within a certain degree.

Elastic matching is applied only to images that pass a composite filtering mechanism, based on spatial relationships matching (for multiple templates) and aspect ratio checking (for each template).

  • A threshold k = 2 has been used for the aspect ratio filtering.
  • The average number of steps of the deformation 

    process depends on how much the image and the 

    sketch shapes are similar. 

  • After 20 steps, the match parameter

    M is compared with a fixed threshold.

  • The neural network that derives the similarity ratings,

    was a three layered 5–12–1 back propagation net.

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