A Novel Representation for Two-dimensional Image Structures

This paper presents a novel approach towards two-dimensional (2D) image structures modeling. To obtain more degrees of freedom, a 2D image signal is embedded into a certain geometric algebra. Coupling methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, we can design a general model for 2D structures as the monogenic extension of a curvature tensor. Based on it, a local representation for the intrinsically two-dimensional (i2D) structure is derived as the monogenic curvature signal. From it, independent features of local amplitude, phase and orientation are simultaneously extracted. Besides, a monogenic curvature scale-space can be built by applying a Poisson kernel to the monogenic curvature signal. Compared with the other related work, the remarkable advantage of our approach lies in the rotationally invariant phase evaluation of 2D structures in a multi-scale framework, which delivers access to phase-based processing in many computer vision tasks

View point robust visual search technique

In this thesis, we have explored visual search techniques for images taken from diferent view points and have tried to enhance the matching capability under view point changes. We have proposed the Homography based back-projection as post-processing stage of Compact Descriptors for Visual Search (CDVS), the new MPEG standard; moreover, we have deined the aine adapted scale space based aine detection, which steers the Gaussian scale space to capture the features from aine transformed images; we have also developed the corresponding gradient based aine descriptor. Using these proposed techniques, the image retrieval robustness to aine transformations has been signiicantly improved. The irst chapter of this thesis introduces the background on visual search. In the second chapter, we propose a homography based back-projection used as the postprocessing stage of CDVS to improve the resilience to view point changes. The theory behind this proposal is that each perspective projection of the image of 2D object can be simulated as an aine transformation. Each pair of aine transformations are mathematically related by homography matrix. Given that matrix, the image can be back-projected to simulate the image of another view point. In this way, the real matched images can then be declared as matching because the perspective distortion has been reduced by the back-projection. An accurate homography estimation from the images of diferent view point requires at least 4 correspondences, which could be ofered by the CDVS pipeline. In this way, the homography based back-projection can be used to scrutinize the images with not enough matched keypoints. If they contain some homography relations, the perspective distortion can then be reduced exploiting the few provided correspondences. In the experiment, this technique has been proved to be quite efective especially to the 2D object images. The third chapter introduces the scale space, which is also the kernel to the feature detection for the scale invariant visual search techniques. Scale space, which is made by a series of Gaussian blurred images, represents the image structures at diferent level of details. The Gaussian smoothed images in the scale space result in feature detection being not invariant to aine transformations. That is the reason why scale invariant visual search techniques are sensitive to aine transformations. Thus, in this chapter, we propose an aine adapted scale space, which employs the aine steered Gaussian ilters to smooth the images. This scale space is lexible to diferent aine transformations and it well represents the image structures from diferent view points. With the help of this structure, the features from diferent view points can be well captured. In practice, the scale invariant visual search techniques have employed a pyramid structure to speed up the construction. By employing the aine Gaussian scale space principles, we also propose two structures to build the aine Gaussian scale space. The structure of aine Gaussian scale space is similar to the pyramid structure because of the similiar sampling and cascading iii properties. Conversely, the aine Laplacian of Gaussian (LoG) structure is completely diferent. The Laplacian operator, under aine transformation, is hard to be aine deformed. Diferently from a simple Laplacian operation on the scale space to build the general LoG construction, the aine LoG can only be obtained by aine LoG convolution and the cascade implementations on the aine scale space. Using our proposed structures, both the aine Gaussian scale space and aine LoG can be constructed. We have also explored the aine scale space implementation in frequency domain. In the second chapter, we will also explore the spectrum of Gaussian image smoothing under the aine transformation, and propose two structures. General speaking, the implementation in frequency domain is more robust to aine transformations at the expense of a higher computational complexity. It makes sense to adopt an aine descriptor for the aine invariant visual search. In the fourth chapter, we will propose an aine invariant feature descriptor based on aine gradient. Currently, the state of the art feature descriptors, including SIFT and Gradient location and orientation histogram (GLOH), are based on the histogram of image gradient around the detected features. If the image gradient is calculated as the diference of the adjacent pixels, it will not be aine invariant. Thus in that chapter, we irst propose an aine gradient which will contribute the aine invariance to the descriptor. This aine gradient will be calculated directly by the derivative of the aine Gaussian blurred images. To simplify the processing, we will also create the corresponding aine Gaussian derivative ilters for diferent detected scales to quickly generate the aine gradient. With this aine gradient, we can apply the same scheme of SIFT descriptor to generate the gradient histogram. By normalizing the histogram, the aine descriptor can then be formed. This aine descriptor is not only aine invariant but also rotation invariant, because the direction of the area to form the histogram is determined by the main direction of the gradient around the features. In practice, this aine descriptor is fully aine invariant and its performance for image matching is extremely good. In the conclusions chapter, we draw some conclusions and describe some future work

Data comparison schemes for Pattern Recognition in Digital Images using Fractals

Pattern recognition in digital images is a common problem with application in remote sensing, electron microscopy, medical imaging, seismic imaging and astrophysics for example. Although this subject has been researched for over twenty years there is still no general solution which can be compared with the human cognitive system in which a pattern can be recognised subject to arbitrary orientation and scale. The application of Artificial Neural Networks can in principle provide a very general solution providing suitable training schemes are implemented. However, this approach raises some major issues in practice. First, the CPU time required to train an ANN for a grey level or colour image can be very large especially if the object has a complex structure with no clear geometrical features such as those that arise in remote sensing applications. Secondly, both the core and file space memory required to represent large images and their associated data tasks leads to a number of problems in which the use of virtual memory is paramount. The primary goal of this research has been to assess methods of image data compression for pattern recognition using a range of different compression methods. In particular, this research has resulted in the design and implementation of a new algorithm for general pattern recognition based on the use of fractal image compression. This approach has for the first time allowed the pattern recognition problem to be solved in a way that is invariant of rotation and scale. It allows both ANNs and correlation to be used subject to appropriate pre-and post-processing techniques for digital image processing on aspect for which a dedicated programmer's work bench has been developed using X-Designer

Left-invariant evolutions of wavelet transforms on the Similitude Group

Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at crossings in an image. To get an overview of how an image is composed of local multiple-scale elongated structures we construct a multiple scale orientation score, which is a continuous wavelet transform on the similitude group, SIM(2). Our unitary transform maps the space of images onto a reproducing kernel space defined on SIM(2), allowing us to robustly relate Euclidean (and scaling) invariant operators on images to left-invariant operators on the corresponding continuous wavelet transform. Rather than often used wavelet (soft-)thresholding techniques, we employ the group structure in the wavelet domain to arrive at left-invariant evolutions and flows (diffusion), for contextual crossing preserving enhancement of multiple scale elongated structures in noisy images. We present experiments that display benefits of our work compared to recent PDE techniques acting directly on the images and to our previous work on left-invariant diffusions on orientation scores defined on Euclidean motion group.Comment: 40 page

Scale Invariant Interest Points with Shearlets

Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities such as edges and corners at multiple scales. In this work we address the problem of detecting and describing blob-like features in the shearlets framework. We derive a measure which is very effective for blob detection and closely related to the Laplacian of Gaussian. We demonstrate the measure satisfies the perfect scale invariance property in the continuous case. In the discrete setting, we derive algorithms for blob detection and keypoint description. Finally, we provide qualitative justifications of our findings as well as a quantitative evaluation on benchmark data. We also report an experimental evidence that our method is very suitable to deal with compressed and noisy images, thanks to the sparsity property of shearlets

Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement

The goal of many early visual filtering processes is to remove noise while at the same time sharpening contrast. An historical succession of approaches to this problem, starting with the use of simple derivative and smoothing operators, and the subsequent realization of the relationship between scale-space and the isotropic dfffusion equation, has recently resulted in the development of "geometry-driven" dfffusion. Nonlinear and anisotropic diffusion methods, as well as image-driven nonlinear filtering, have provided improved performance relative to the older isotropic and linear diffusion techniques. These techniques, which either explicitly or implicitly make use of kernels whose shape and center are functions of local image structure are too computationally expensive for use in real-time vision applications. In this paper, we show that results which are largely equivalent to those obtained from geometry-driven diffusion can be achieved by a process which is conceptually separated info two very different functions. The first involves the construction of a vector~field of "offsets", defined on a subset of the original image, at which to apply a filter. The offsets are used to displace filters away from boundaries to prevent edge blurring and destruction. The second is the (straightforward) application of the filter itself. The former function is a kind generalized image skeletonization; the latter is conventional image filtering. This formulation leads to results which are qualitatively similar to contemporary nonlinear diffusion methods, but at computation times that are roughly two orders of magnitude faster; allowing applications of this technique to real-time imaging. An additional advantage of this formulation is that it allows existing filter hardware and software implementations to be applied with no modification, since the offset step reduces to an image pixel permutation, or look-up table operation, after application of the filter

A preliminary approach to intelligent x-ray imaging for baggage inspection at airports

Identifying explosives in baggage at airports relies on being able to characterize the materials that make up an X-ray image. If a suspicion is generated during the imaging process (step 1), the image data could be enhanced by adapting the scanning parameters (step 2). This paper addresses the first part of this problem and uses textural signatures to recognize and characterize materials and hence enabling system control. Directional Gabor-type filtering was applied to a series of different X-ray images. Images were processed in such a way as to simulate a line scanning geometry. Based on our experiments with images of industrial standards and our own samples it was found that different materials could be characterized in terms of the frequency range and orientation of the filters. It was also found that the signal strength generated by the filters could be used as an indicator of visibility and optimum imaging conditions predicted