Wigner distribution representation of digital images

Wigner distribution and entropy of partially coherent light generated by perfect optical vortices

We developed analytical expressions for the Wigner distribution function of partially coherent fields generated by the scattering of beams with a particular phase structure, namely perfect optical vortex beams. In addition, we provide the modal decomposition of the field correlations and evaluate the evolution of Shannon entropy associated with the partially coherent field.

Real-time generation of the Wigner distribution of complex functions using phase conjugation in photorefractive materials

An optical processor for real-time generation of the Wigner distribution of complex amplitude functions is introduced. The phase conjugation of the input signal is accomplished by a highly efficient self-pumped phase conjugator based on a 45 degrees -cut barium titanate photorefractive crystal. Experimental results on the real-time generation of Wigner distribution slices for complex amplitude two-dimensional optical functions are presented and discussed.

Optical digital implementation of the Wigner distribution function: use in space variant filtering of real images

An optical digital processor based on the Wigner distribution function (WDF) has been implemented, permitting space variant filtering of 2-D real images. The processor sequentially generates all space samples of the distribution; thus, each sample can be modified by a different filter. The filtered Wigner distribution function is optically inverted, and a digital image processor selects the information associated with each sample of the image. Compared to a digital implementation, the required computer time has been reduced to the point where future practical use of Wigner filtering can be expected.

Space-variant filtering through the Wigner distribution function

Space-invariant and space-variant filtering of discrete images with unidimensional variation is performed in this paper through the Wigner distribution function (WDF). Low-pass, bandpass, and high-pass filtering is used in the Fourier domain and in the Wigner distribution, to compare their different behavior in both cases. A space-variant filter is generated to modify the WDF of an object to obtain, after inversion, a spatially variant filtered image. Finally, spatially variant defocused images generated through the Wigner distribution are restored by Wiener based filters applied in the Wigner domain. The method applied to recover the filtered images can easily be generalized to bidimensional images.

Image analysis through the Wigner distribution function

The Wigner distribution (WD) for discrete images is computed and applied for texture analysis. First, the WD for different test images with spatial frequency and gray level information content is computed, and the most important features of the WD are outlined. Likewise, the original image with 1-D variation is recovered from the discrete WD; local filtering operations have been performed on the distribution, and a filtered version of the original image is then obtained. Since the WD entails simultaneous representation of the intensity distribution and of the spatial interdependence, it seems specially adequate for processing of textured information. In this way, texture recognition is performed through the extraction of features from the WD, and the results are compared with other methods. Finally, to avoid the great computational effort that requires this kind of representation, a hybrid optical-digital processing system is proposed for the texture recognition process.