Understanding this Gabor Filter equation
I will describe the rationale behind the "non-standard" terms, with respect to more classical expressions. 

Essentialy, the $\omega e^{-\omega^2 }$ term indicates a derivative of a Gaussian (with 0 average), similar to an antisymmetric wavelet, instead of the modulated Gaussian window in standard Gabor filters: a wavelet filter bank, versus a modulated filter banks. This wavelet "smoothed derivative" aspect might help detect edges. 

Then, the $4a^2+b^2$ induces an elliptic shape constraining anisotropy in the 2D wavelet, with a $2$-fold factor ratio.  

Last, the $e^{-c^2/2}$ might serve an admissibility condition for this Morlet-Gabor like wavelet, to ensure easier inversion/reconstruction.

It is truly multiscale, as they specify they have 5 dyadic scales.