Applications of the SIG
The Sphere-of-Influence graph can be applied to many areas of Computer Vision, Pattern Recognition, Data Mining and many others. For example:
- In Computer Vision for object recognition, from input dot patterns.
In vision applications, the SIG can be used as a low-level operator. This means, to perform some sort of preprcoessing on the input before feeding it , into a higher level algorithm, the SIG can be used to improve data quality and remove spurious inputs.
- Clustering objects with similar attribute values in data mining applications.
Clustering is a technique of data mining, where the data values are grouped together based on similarities in one or more of their attribute values. Clustering helps to organize and "group-together" objects that has similarity between each other according to some measurement.
The SIG has been known to aid in providing graph-theoretic explanations to some optical illusions.
For example, the following illusion, known as the Mueller-Lyer illusion in literature, has a line segment with opposite-facing arrows attached to each end. These two lines are of equal length, although we perceive the one with the arrows "angled-in" (or "pointing-out") to be shorter (figure A, below). Measuring the length of the central vertical line connecting the portions of the SIG where they branch out, we see that the line segment so obtained is indeed shorter in figure (A) below than in figure (B). If the angles of the arrowheads are made more acute, then the magnitude of the illusion decreases as in agreement with empirical evidence. The SIG thus provides one explanation of the illusion as perceived by the human visual system.
The Mueller-Lyer Illusion and the SIG
Recently in Computer Graphics, the SIG and other proximity graphs have been looked into for defining surfaces over point clouds.
Surfaces over noisy point cloudes can used for data visualization, shape reconstruction, texture generation etc. Particularly in , the authors use a special type of SIG known as the r-SIG, where instead of considering the nearest neighbour for constructing the circle, the distance to the r-th nearest neighbour is taken.