We present an improved and optimized formulation for the estimation of the multiscale amplitude-modulation frequency-modulation (AM-FM) estimates when (i) non-separable filters are used and (ii) the variable spacing, local linear phase method is used. Also, we introduce the use of multiscale directional filterbanks for the feature extraction of images. Recently, AM-FM methods have shown promising results in a variety of medical image analysis applications. The 2D optimized AM-FM demodulation described here presents advantages for feature extraction at different frequency scales and orientations that can be used to detect different patterns, directions, or structures in an image. We test the new formulation using a Gaussian amplitude-modulated Quadratic frequency-modulated synthetic image and natural images. The results show that the optimized estimation produces better results, up to 4.9 times for the IF estimation and in 3 orders of magnitude for the IA estimation, for noise-free signals compared to the state-of-the-art methods.