Deriving scale normalisation factors for a GLoG detector

Abstract

In computer vision, blob detection is used to obtain regions of interest that could signal the presence of objects or parts with application to object recognition and object tracking. One of the more common blob detectors is based on the Laplacian of Gaussian (LoG). However, most blob detectors developed in the past assume circular blobs, and these detectors do not perform as well with elliptical blobs, a more prevalent scenario in real images. A generalised LoG (GLoG) detector was proposed recently to deal specifically with elliptical blobs. To formulate the GLoG in a multi-scale framework, its response must be made scale invariant. Toward that end, necessary and sufficient conditions are presented here, with the normalisation factors derived for a scale-invariant GLoG detector. The factors are validated with a synthetic example and are further tested with two real-world images.