Blob Detection - The Difference of Gaussians Approach

The Difference of Gaussians Approach

From the fact that the scale space representation satisfies the diffusion equation

it follows that the Laplacian of the Gaussian operator can also be computed as the limit case of the difference between two Gaussian smoothed images (scale space representations)

$\begin{align} \nabla^2_{norm} L(x, y; t) &\approx \frac{t}{\Delta t} \left( L(x, y; t+\Delta t) - L(x, y; t-\Delta t) \right) \end{align}$ .

In the computer vision literature, this approach is referred to as the Difference of Gaussians (DoG) approach. Besides minor technicalities, however, this operator is in essence similar to the Laplacian and can be seen as an approximation of the Laplacian operator. In a similar fashion as for the Laplacian blob detector, blobs can be detected from scale-space extrema of differences of Gaussians -- see Lindeberg (2012) for the explicit relation between the difference-of-Gaussian operator and the scale-normalized Laplacian operator.

Read more about this topic: Blob Detection

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