Donald J. Bone

Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform

It is widely believed, in the areas of optics, image analysis, and visual perception, that the Hilbert transform does not extend naturally and isotropically beyond one dimension. In some areas of image analysis, this belief has restricted the application of the analytic signal concept to multiple dimensions. We show that, contrary to this view, there is a natural, isotropic, and elegant extension. We develop a novel two-dimensional transform in terms of two multiplicative operators: a spiral phase spectral (Fourier) operator and an orientational phase spatial operator. Combining the two operators results in a meaningful two-dimensional quadrature (or Hilbert) transform. The new transform is applied to the problem of closed fringe pattern demodulation in two dimensions, resulting in a direct solution. The new transform has connections with the Riesz transform of classical harmonic analysis. We consider these connections, as well as others such as the propagation of optical phase singularities and the reconstruction of geomagnetic fields.

Fringe-pattern analysis using a 2-D Fourier transform

A refinement of the Fourier transform fringe-pattern analysis technique which uses a 2-D Fourier transform is described. The 2-D transform permits better separation of the desired information components from unwanted components than a 1-D transform. The accuracy of the technique when applied to real data recorded by a system with a nonlinear response function is investigated. This leads to simple techniques for optimizing an interferogram for analysis by these Fourier transform methods and to an estimate of the error in the retrieved fringe shifts. This estimate is tested on simulated data and found to be reliable.

Fourier fringe analysis: the two-dimensional phase unwrapping problem

A new phase unwrapping algorithm is described that uses local phase information to mask out those parts of the field that cause inconsistencies in the unwrapping. Unlike earlier techniques, which produce only a consistent unwrapping of the phase in the presence of discontinuities, this technique can produce an approximately correct unwrapping. The technique is tolerant of discontinuities and noise in the phase and is fast, efficient, and simple to implement. In the absence of discontinuities an rms signal-to-noise ratio in the wrapped phase of <2:1 can be tolerated.

Skin colour region detection in MPEG video sequences

Efficient indexing and retrieval of digital video data is an important aspect of video database management. Video indexing involves content analysis of video sequences, which is usually a computationally intensive process. Since most video data is stored in compressed format, processing directly in the compressed domain offers the possibility of computationally more efficient algorithms. We present here an efficient algorithm for detecting skin colour regions directly in MPEG video sequences. Most existing methods for skin colour detection usually threshold some sort of measure of the likelihood of skin colours for each pixel and treat them independently. Our algorithm takes the spatial neighbourhood information of each block into account by performing region growing for those blocks with a high probability of belonging to the skin colour class, since skin colour blocks usually appear as contiguous regions in an image. A novel method for finding an adaptive threshold to control the region growing process is also presented, which incorporates the edge information into the segmentation. Experimental results on several video sequences show that the proposed algorithm is able to detect skin colour regions in MPEG video sequences with various scene complexities.

Computational fluid dynamics validation using multiple interferometric views of a hypersonic flowfield

The validity of the computed three-dimensional perfect-gas inviscid density field of the shock layer about a blunt body in a hypersonic argon freestream has been investigated. Mach-Zehnder interferometry was used to generate interferograms of such a flowfield produced in the T3 free-piston shock tunnel. Two-dimensional phase maps (representing line-of-sight integrated density) were produced from the interferograms using a two-dimensional Fourier transform fringe analysis method. Theoretical maps, computed from the computational fluid dynamics solution, compare extremely well with experimental maps for each of seven different viewing angles used to generate interferograms. The multiple angles remove the ambiguity associated with comparing theoretical and experimental integrated quantities. Thus, confidence can be placed in the validity of the three-dimensional density computations.

Replay Detection in Sports Video Sequences

In many sports, the majority of highlights are confined to relatively short durations of intense action. In some sense these segments capture the essence of a game and summarize the moments of important action. Automatic detection of these highlights could provide an important browsing mechanism in a video library of sports games. In this paper, we present efficient algorithms, operating in the MPEG domain, for detecting two kinds of replay from sports video sequences. These replays often correspond to highlights in a game and can be used as indices of a sports video. The first algorithm detects exact replays while the second algorithm detects slow motion replays. Both algorithms operate directly on MPEG-1/MPEG-2 video data and thus they are very efficient because the expensive decoding operation is unnecessary. Experimental results on several video sequences show that the proposed algorithms are effective in detecting replays in most sports video sequences.

Orthonormal Fractal Image Encoding Using Overlapping Blocks

This paper presents a novel approach to partitioned fractal image encoding. In this we seek to address a number of problems with earlier fractal encodings. These are: the artefacts associated with the block based approaches at high compression ratios; accuracy limitations imposed by the constraint that only one domain block is used to construct each range block; convergence problems which have required that constraints be imposed on the scaling coefficients to ensure that the mapping functions are contractive. These problems are addressed with a technique based on an orthonormal basis expansion using overlapping blocks, where the basis is partly fixed and partly derived from the image in such a way as to take advantage of local interscale self similarity. A fractal image codec based on this technique, which we call the Lapped Orthogonal Fractal Transform (LOFT), is described and tested, and the results are compared to those of other codecs.

Electro-optic modulation using Fabry-Pérot etalons containing a poled crosslinked polymer

Abstract Fabrication and characterisation of electro-optic Fabry-Perot modulators containing a poled crosslinked polymer are described. Electro-optic modulation as large as 38% in reflection has been obtained with a low cavity finesse figure of 3.4 and a driving voltage of 88 V rms. The corresponding electro-optic coefficients r13 and r33 were measured at 633 nm to be 11 pm/V and 36 pm/V using angle-tuning of the Fabry-Perot etalon. The thermo-optical coefficient of 1.0×10-4 K-1 of the polymer film was also measured. A lower-bound measure of the bandwidth of these devices was observed at a detection system limit of 1 MHz.

Adaptive color-printer modeling using regularized linear splines

The characterization of a highly non-linear color print device can involve a large number of measurements of printed color output. If the measurement process is not automated this can be a significant fraction of the cost of developing a color model for a device. One way to limit the number of measurements required is to ensure that in any given region, only enough measurements are made to adequately characterize the local behavior. With no prior knowledge of the behavior, this requires an adaptive approach to the sampling. An adaptive sampling technique developed for this work, termed Model Accuracy Moderated Adaptive Sampling (MAMAS), is described. Simulation tests with and without measurement noise are presented and the results are compared to measurements using uniform regular sampling. The technique is also applied to a real printer, the Canon CLC500, for which some results are presented. The color model used for the print device is based on an interpolated look up table (ILUT). Because of the highly non-linear nature of the device being modeled a flexible technique is required to translate the irregular measurement samples into a regularly gridded model. A method based on a regularized linear spline was developed. Appropriate choice of the penalty function for the regularization can achieve a compromise between fitting the measured points and reducing the impact of measurement noise. A brief overview of the technique is presented.

Spectral line interferometry with temporal and spatial resolution

Abstract A novel application of spectral line interferometry, giving spatial and temporal resolution of an atomic level population for a single event, is presented. Automated and accurate analysis of the interferogram is demonstrated using a fringe pattern analysis based on a two-dimensional Fourier transform. A measurement of an atomic level population in a laser produced barium plasma is used to illustrate these techniques.