Introduction. 1. Two Dimensional Systems and Mathematical Preliminaries. 2. Image Perception. 3. Image Sampling and Quantization. 4. Image Transforms. 5. Image Representation by Stochastic Models. 6. Image Enhancement. 7. Image Filtering and Restoration. 8. Image Analysis and Computer Vision. 9. Image Reconstruction From Projections. 10. Image Data Compression.

Fundamentals of digital image processing

In this survey, we review work in machine learning on methods for handling data sets containing large amounts of irrelevant information. We focus on two key issues: the problem of selecting relevant features, and the problem of selecting relevant examples. We describe the advances that have been made on these topics in both empirical and theoretical work in machine learning, and we present a general framework that we use to compare different methods. We close with some challenges for future work in this area. @ 1997 Elsevier Science B.V.

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Selection of relevant features and examples in machine

The problem of rotation-, scale-, and translation-invariant recognition of images is discussed. A set of rotation-invariant features are introduced. They are the magnitudes of a set of orthogonal complex moments of the image known as Zernike moments. Scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments. A systematic reconstruction-based method for deciding the highest-order Zernike moments required in a classification problem is developed. The quality of the reconstructed image is examined through its comparison to the original one. The orthogonality property of the Zernike moments, which simplifies the process of image reconstruction, make the suggest feature selection approach practical. Features of each order can also be weighted according to their contribution to the reconstruction process. The superiority of Zernike moment features over regular moments and moment invariants was experimentally verified. >

Invariant image recognition by Zernike moments

This correspondence discusses an extension of the well-known phase correlation technique to cover translation, rotation, and scaling. Fourier scaling properties and Fourier rotational properties are used to find scale and rotational movement. The phase correlation technique determines the translational movement. This method shows excellent robustness against random noise.

An FFT-based technique for translation, rotation, and scale-invariant image registration

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*This new edition now contains essential information on steganalysis and steganography
*New concepts and new applications including QIM introduced
*Digital watermark embedding is given a complete update with new processes and applications

Digital Watermarking and Steganography

Presented in this paper is an optical implementation of a shift- and rotation-invariant pattern recognition technique. A computer-generated hologram is designed to match with one of the circular harmonic components of the target. Experimental results with simple photographic objects show that targets with different locations and orientations can be simultaneously recognized by the optical system.

Optical pattern recognition using circular harmonic expansion

Image descriptors based on the circular-Fourier-radial-Mellin transform are used for position-, rotation-, scale-, and intensity-invariant multiclass pattern recognition. The orders of the radial moments and of the circular harmonics are chosen to obtain an efficient image description. The first-order radial moments of three circular harmonics are sufficient to obtain a satisfactory recognition performance. The influence of additive noise is investigated. Experimental results are shown.

https://www.intranet.copl.ulaval.ca/sheng/publications/JsaA3p771-FMM.pdf

Experiments on pattern recognition using invariant Fourier-Mellin descriptors.

A new method has been developed for rotation-invariant pattern recognition. One component of the circular harmonic expansion of the target is used in the preparation of the reference. Correlations between the input and reference objects are accomplished by FFT and multiplication in the frequency domain. In an experience with targets from an image with 192 × 192 pixels, target orientations were detected with an accuracy of ~0.1°. This method is also suitable for optical implementation.

Rotation-invariant digital pattern recognition using circular harmonic expansion.

When image plane speckle intensity integrated over a finite aperture is submitted to a logarithmic transformation, the noise becomes additive and signal independent. The first- and second-order moments of the probability distribution are derived. It is found that the logarithm of speckle noise approaches a normal distribution much faster than speckle intensity. The properties of speckle noise are different from those of film-grain noise; for example, neither Nutting’s law nor Selwyn’s law is satisfied by speckle.

Properties of speckle integrated with a finite aperture and logarithmically transformed

The properties of the amplitude and illuminance of the images of coherently illuminated diffuse objects are studied. Uniform and nonuniform objects are considered. The image illuminance is considered to result from a linear transformation of a nonstationary gaussian stochastic process followed by a square-law detection. Expressions are obtained for the mean, autocorrelation, variance, and spatial power spectral density of the amplitude and of the illuminance. Interpretation of the results led to conclusions concerning the speckle size, the noise power in the image, and the transfer function of an optical system when the object diffuses coherent light. When the autocorrelation width of the random fluctuations of the object amplitude is small compared to the impulse response of the system, the mean illuminance in the image plane is that which would be given by an incoherent object having the same luminance as the object considered; the average speckle size is equal to that of the impulse response of the system; the average transfer function of the system is the incoherent transfer function; and the distribution of the noise spatial frequencies does not depend upon the form of the signal, but only upon its total energy. Other results concerning the image statistics have also been obtained.

Henri H. Arsenault

Papers

Optical pattern recognition using circular harmonic expansion

Experiments on pattern recognition using invariant Fourier-Mellin descriptors.

Rotation-invariant digital pattern recognition using circular harmonic expansion.

Properties of speckle integrated with a finite aperture and logarithmically transformed

Image Formation for Coherent Diffuse Objects: Statistical Properties