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Shape analysis using fractal dimension: A curvature based approach
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Image of FIG. 1.
FIG. 1.

(a) Fish contour; (b) curvature scale space represented in a gray-scale image: the greater the curvature, the brighter the pixel in the image.

Image of FIG. 2.
FIG. 2.

Smoothing of a shape contour as the parameter changes.

Image of FIG. 3.
FIG. 3.

Process of shape dilation of the Bouligand-Minkowski method (light gray, points correspondent to the current radius r; dark gray, accumulated area): (a) Original shape (r = 0); (b) ; (c) ; (d) .

Image of FIG. 4.
FIG. 4.

(a) Koch snowflake (d = 1.2618); (b) curvature fractal dimension (d =1.2644).

Image of FIG. 5.
FIG. 5.

(a) Log-log curve. (b) multi-scale fractal dimension.

Image of FIG. 6.
FIG. 6.

Examples of fish images used in the experiments.

Image of FIG. 7.
FIG. 7.

(a) Bouligand-Minkowski log-log curve. (b) Bouligand-Minkowski multi-scale fractal dimension.

Image of FIG. 8.
FIG. 8.

Success rate according to the number of descriptors used.

Image of FIG. 9.
FIG. 9.

Curvature and the sum of its coefficients, , for two contour at different scales.


Generic image for table
Table I.

Comparison results for different complexity estimation methods.

Generic image for table
Table II.

Comparison results for other non-fractal shape analysis methods.


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Scitation: Shape analysis using fractal dimension: A curvature based approach