Descriptive Statistics Parameters of Normalized Edge-To-Centroid Distances as a Shape Feature that is Rotation and Scale Invariant

In Computer Vision, Shape Feature is one of the important features besides color and texture. A Geometric type of Shape Features uses parameters from the Region of Interest as the input such as Area, bounding rectangle's width and length, Axis Length, Centroid, and Perimeter. The Rectangularity, the Eccentricity, and the Elongation rely on the bounding rectangle which is invariant to rotation. The Circularity is invariant to rotation and scale but only captures the general information of the object's area. This research proposes a basic Shape Feature that is rotation and scale invariant. First, it finds the centroid of the Region of Interest using the Moment equation, then it finds the edges using the Sobel operator and calculates the distances between them. The distance uses Euclidian Distance that is invariant to rotation. The distance values are normalized using the Min-Max Normalization to maintain their value due to scale variations. Descriptive Statistics such as Mean, Median, Standard Deviation, Skewness, and Kurtosis are used as the parameter extracted from the normalized distances. The proposed shape feature is tested in common planar shapes with different sizes and rotations such as circle, oval, square, rectangle, triangle, and pentagon and it shows good grouping. The features can cluster the different shapes with a Silhouette Index of 0.578.