H.H. Arsenault

Rotation and scale invariance with polar and log-polar coordinate transformations

Abstract The optical implementation by means of holographic optical elements of polar and log-polar coordinate transformations (CTs) for rotation and scale invariant pattern recognition is attractive to achieve real-time processing of input scenes. The quality of the CTs realized so far and the image wrapping problem have limited this method to the processing of the most simple objects. We propose a new CT implementation with computer generated holograms partioned into non-uniform facets. The hologram recording is done with a commercial photo-typesetter at a very low cost. The image wrapping problem is alleviated by means of juxtaposed CTs. The intensity of the Fourier transform of the CTs is used to correctly classify the objects, and only this classification step was done numerically in our experiment. Optical results are presented and demonstrate the quality of our CTs.

A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition [Opt. Commun. 172 (1999) 181–192]

Abstract A new sliced orthogonal nonlinear generalized (SONG) decomposition for image processing can be useful for image representation. We examine the use of this representation for two-class pattern recognition in the presence of noise. The SONG correlation is defined and expressed by means of a diagonal matrix representation. Common linear correlation, binary correlation and morphological correlation, among others, can be described in terms of the SONG representation. This matrix allows the investigation of some interesting properties of auto-correlation and cross-correlation operations. The discrimination capability and noise robustness of the SONG correlation are investigated and compared with those of other methods. Experimental results establish the stability of the SONG process at Gaussian noise levels high enough for the other methods to break down. Although the pattern recognition method is nonlinear, the elementary correlation operations are linear and so the method is suitable for optical implementation.

Methods for reducing sidelobes associated with composite filters

Abstract We propose two new methods for reducing sidelobes associated with pattern recognition using composite filters, which are linear combinations of matched filters. The recognition of objects on uniform and on cluttered backgrounds are both discussed. Experiments on aircraft comparing these methods with previously published methods indicate that the new methods yield the best results.

Les effets causes par les dimensions de la source dans les systemes optiques eclaires en lumiere spatialement incoherente

Abstract It has been shown recently that in order for an incoherent optical system to be linear and space invariant, the image of the source at the filter plane must be larger than the filter aperture. We show in this paper that the source image must be larger than the filter by an amount equal to twice the highest spatial frequency of the object, the frequency being measured in the filter plane.

Random bias holograms

Abstract To make holograms of three-dimensional diffuse objects, the conventional technique consists of illuminating the photographic plate with a uniform reference beam that is modulated by the light reflected from the object. This set-up requires a number of beam splitters, beam expanders, pinhole filters and mirrors. If instead of a uniform reference beam, we use a reference beam having large random variations of amplitude from point to point, it is still possible under certain conditions to reconstruct the object from the hologram. A method is described for making holograms of three-dimensional objects using only a laser, one mirror, one diffuser, and a photographic plate. Such holograms may be reconstructed with a point source in the usual manner, and the quality of the image is comparable to that from ordinary holograms.

Optical circular sampling system for translation and rotation invariant pattern recognition

Abstract A simple but effective rotation invariant pattern recognition method based on optical circular sampling of the input pattern is described. The object is decomposed by a set of concentric rings. The distribution of energy between those rings is independent of the orientation of the object and characterizes it sufficiently to allow its classification. A computer generated hologram formed of concentric diffraction grating rings of suitable spatial frequencies may perform the sampling in parallel. In combination with a lens, each ring is then focused to a given position on a CCD detector where the intensity distribution may be found. Translation invariance is added to the system by sampling the intensity of the Fourier transform of the input object in combination with a liquid crystal light valve. A phototypesetter is used to write the hologram whose quality is demonstrated by optical experiments.

Statistical properties of speckle recorded on film

Abstract The statistical properties of speckle recorded on photographic film are studied theoretically and experimentally. When saturation and threshold effects are negligible and the gamma is equal to one, the probability distribution function of spatially integrated film transmittance has the form of a double exponential. Experimental results confirm that under those conditions, the density fluctuations caused by the speckle are independent of the signal.

Recent results in rotation-invariant pattern recognition

This paper reviews recent progress in rotation invariant pattern recognition; the emphasis is on the work done in our own laboratories, since much of the significant work done elsewhere is described in other papers presented at this conference.

Linearity and space invariance in superresolving systems

Abstract It is shown that for superresolving systems having the properties of linearity and space invariance, the spread function is not always equal to the impulse response. The spread function and impulse response are calculated for a typical system, and are shown to be different. It follows that the spread function of such a system may not be found by determining the response when the object is a point source.

Comparative performance of locally nonlinear matched filters and of optimal tradeoff filters

A comparison of the performance of Locally Nonlinear Filters (LNMFs) and Optimal Tradeoff Filters (OTFs) for the recognition of single images has been carried out. The comparison is done using several performance criteria such as Signal to Noise Ratio, Peak to Correlation Energy Ratio and Optical Efficiency. A strong similarity between the whitening strategies of both filter families has been found when the Optimal Tradeoff Filters for peak sharpness and noise robustness are compared with LNMFs. Our tests show a marginal superiority of OTFs over LNMFs.