A Generalized Laplacian of Gaussian Filter for Blob Detection and Its Applications

In this paper, we propose a generalized Laplacian of Gaussian (LoG) (gLoG) filter for detecting general elliptical blob structures in images. The gLoG filter can not only accurately locate the blob centers but also estimate the scales, shapes, and orientations of the detected blobs. These functions can be realized by generalizing the common 3-D LoG scale-space blob detector to a 5-D gLoG scale-space one, where the five parameters are image-domain coordinates (x, y), scales (sigma(x), sigma(y)), and orientation (theta), respectively. Instead of searching the local extrema of the image's 5-D gLoG scale space for locating blobs, a more feasible solution is given by locating the local maxima of an intermediate map, which is obtained by aggregating the log-scale-normalized convolution responses of each individual gLoG filter. The proposed gLoG-based blob detector is applied to both biomedical images and natural ones such as general road-scene images. For the biomedical applications on pathological and fluorescent microscopic images, the gLoG blob detector can accurately detect the centers and estimate the sizes and orientations of cell nuclei. These centers are utilized as markers for a watershed-based touching-cell splitting method to split touching nuclei and counting cells in segmentation-free images. For the application on road images, the proposed detector can produce promising estimation of texture orientations, achieving an accurate texture-based road vanishing point detection method. The implementation of our method is quite straightforward due to a very small number of tunable parameters.