The Fourier transform is a century-old mathematical theory. Among many of its applications, it has been the foundation of signal processing since the middle of 20th century. Specifically, it has been hugely successful to perform voice recognition using frequency spectrum. However, its application in 2D image analysis is limited. This observation motivated the research presented in this thesis. Most natural images contain non-stationary signals that require local image analysis techniques. The primary approach is the Short Time Fourier Transform (STFT), most notably the Gabor transform. A critical analysis presented in this thesis reveals that Gabor transform produces a spectrum with frequency resolution depending on the window width. In addition, the discrete sampling positions in the frequency domain are also varying due to the change of the window width. A novel technique, called probing detector, is proposed in this thesis to overcome these problems. The probing detector produces a spectrum with the highest possible frequency resolution and consistent discrete sampling positions in the frequency domain.