Showing papers by "Patrick Vandewalle published in 2006"

A frequency domain approach to registration of aliased images with application to super-resolution

Abstract: Super-resolution algorithms reconstruct a high-resolution image from a set of low-resolution images of a scene. Precise alignment of the input images is an essential part of such algorithms. If the low-resolution images are undersampled and have aliasing artifacts, the performance of standard registration algorithms decreases. We propose a frequency domain technique to precisely register a set of aliased images, based on their low-frequency, aliasing-free part. A high-resolution image is then reconstructed using cubic interpolation. Our algorithm is compared to other algorithms in simulations and practical experiments using real aliased images. Both show very good visual results and prove the attractivity of our approach in the case of aliased input images. A possible application is to digital cameras where a set of rapidly acquired images can be used to recover a higher-resolution final image.

Super-resolution from unregistered aliased images

Abstract: Aliasing in images is often considered as a nuisance. Artificial low frequency patterns and jagged edges appear when an image is sampled at a too low frequency. However, aliasing also conveys useful information about the high frequency content of the image, which is exploited in super-resolution applications. We use a set of input images of the same scene to extract such high frequency information and create a higher resolution aliasing-free image. Typically, there is a small shift or more complex motion between the different images, such that they contain slightly different information about the scene. Super-resolution image reconstruction can be formulated as a multichannel sampling problem with unknown offsets. This results in a set of equations that are linear in the unknown signal coefficients but nonlinear in the offsets. This thesis concentrates on the computation of these offsets, as they are an essential prerequisite for an accurate high resolution reconstruction. If a part of the image spectra is free of aliasing, the planar shift and rotation parameters can be computed using only this low frequency information. In such a case, the images can be registered pairwise to a reference image. Such a method is not applicable if the images are undersampled by a factor of two or larger. A higher number of images needs to be registered jointly. Two subspace methods are discussed for such highly aliased images. The first approach is based on a Fourier description of the aliased signals as a sum of overlapping parts of the spectrum. It uses a rank condition to find the correct offsets. The second one uses a more general expansion in an arbitrary Hilbert space to compute the signal offsets. The sampled signal is represented as a linear combination of sampled basis functions. The offsets are computed by projecting the signal onto varying subspaces. Under certain conditions, in particular for bandlimited signals, the nonlinear super-resolution equations can be written as a set of polynomial equations. Using Buchberger's algorithm, the solution can then be computed as a Grobner basis for the corresponding polynomial ideal. After a description of a standard algorithm, adaptations are made for the use with noisy measurements. The techniques presented in this thesis are tested in simulations and practical experiments. The experiments are performed on sets of real images taken with a digital camera. The results show the validity of the algorithms: registration parameters are computed with subpixel precision, and aliasing is accurately removed from the resulting high resolution image. This thesis is produced according to the concepts of reproducible research. All the results and examples used in this thesis are reproducible using the code and data available online.

Automatic Red-Eye Removal based on Sclera and Skin Tone Detection

Abstract: It is well-known that taking portrait photographs with a built in camera may create a red-eye effect. This effect is caused by the light entering the subject’s eye through the pupil and reflecting from the retina back to the sensor. These red eyes are probably one of the most important types of artifacts in portrait pictures. Many different techniques exist for removing these artifacts digitally after image capture. In most of the existing software tools, the user has to select the zone in which the red eye is located. The aim of our method is to automatically detect and correct the red eyes. Our algorithm detects the eye itself by finding the appropriate colors and shapes without input from the user. We use the basic knowledge that an eye is haracterized by its shape and the white color of the sclera. Combining this intuitive approach with the detection of “skin” around the eye, we obtain a higher success rate than most of the tools we tested. Moreover, our algorithm works for any type of skin tone. The main goal of this algorithm is to accurately remove red eyes from a picture, while avoiding false positives completely, which is the biggest problem of camera integrated algorithms or distributed software tools. At the same time, we want to keep the false negative rate as low as possible. We implemented this algorithm in a web-based application to allow people to correct their images online.

Signal Reconstruction From Multiple Unregistered Sets Of Samples Using Groebner Bases

Abstract: We present a new method for signal reconstruction from multiple sets of samples with unknown offsets. We rewrite the reconstruction problem as a set of polynomial equations in the unknown signal parameters and the offsets between the sets of samples. Then, we construct a Grobner basis for the corresponding affine variety. The signal parameters can then easily be derived from this Grobner basis. This provides us with an elegant solution method for the initial nonlinear problem. We show two examples for the reconstruction of polynomial signals and Fourier series.

Registration of aliased images for super-resolution imaging

Abstract: Super-resolution imaging techniques reconstruct a high resolution image from a set of low resolution images that are taken from almost the same point of view. The problem can be subdivided into two main parts: an image registration part where the different input images are aligned with each other, and a reconstruction part, where the high resolution image is reconstructed from the aligned images. In this paper, we mainly consider the first step: image registration. We present three frequency domain methods to accurately align a set of undersampled images. First, we describe a registration method for images that have an aliasing-free part in their spectrum. The images are then registered using that aliasing-free part. Next, we present two subspace methods to register completely aliased images. Arbitrary undersampling factors are possible with these methods, but they have an increased computational complexity. In all three methods, we only consider planar shifts. We also show the results of these three algorithms in simulations and practical experiments.

Aliasing is Good for You: Joint Registration and Reconstruction for Super-Resolution

Abstract: In many applications, the sampling frequency is limited by the physical characteristics of the components: the pixel pitch, the rate of the A/D converter, etc A low-pass filter is then often applied before the sampling operation to avoid aliasing However, when multiple copies are available, it is possible to use the information that is inherently present in the aliasing to reconstruct a higher resolution signal If the different copies have unknown relative offsets, this is a non-linear problem in the offsets and the signal coefficients They are not easily separable in the set of equations describing the super-resolution problem Thus, we perform joint registration and reconstruction from multiple unregistered sets of samples We give a mathematical formulation for the problem when there are M sets of N samples of a signal that is described by L expansion coefficients We prove that the solution of the registration and reconstruction problem is generically unique if MN >= L+M-1 We describe two subspace-based methods to compute this solution Their complexity is analyzed, and some heuristic methods are proposed Finally, some numerical simulation results on one and two-dimensional signals are given to show the performance of these methods