||I will give a brief overview of the results presented in my PhD thesis.
A general goal for the research has been to develop shape analysis methods
that can be applied to fuzzy segmented images in 2D and 3D. We have studied
representation and reconstruction of a shape by using moments of both its
crisp and fuzzy discretization.
We show, both theoretically and statistically, that the precision of
estimation of moments of a shape is increased if a fuzzy representation of
a shape is used, instead of a crisp one. The signature of a shape based on
the distance from the shape centroid is studied and two approaches for its
calculation for fuzzy shapes are proposed. A comparison of the performance
of fuzzy and crisp approaches is carried out through a statistical study,
where a higher precision of shape signature estimation is observed for the
fuzzy approaches. The measurements of area, perimeter, and compactness, as
well as of volume, surface area, and sphericity, are considered, too.
New methods are developed for the estimation of perimeter and surface area
of a discrete fuzzy shape. It is shown through statistical studies that the
precision of all the observed estimates increases if a fuzzy representation
is used and that the improvement is more significant at low spatial
resolutions. In addition, a defuzzification method based on feature
invariance is designed, utilizing the improved estimates of shape
characteristics from fuzzy sets to generate crisp discrete shapes with the
most similar shape characteristics.