Luca Lucchese

A noise-robust frequency domain technique for estimating planar roto-translations

This work presents a new method for estimating planar roto-translations that operates in the frequency domain and as such, is not based on features. Since the proposed technique uses all the image information, it is very robust against noise, it can be very accurate; estimation errors on the rotational angle varies from a few hundredths to a few tenths of a degree, depending on the noise level. Experimental evidence of this performance is presented, and the mathematical reasons behind these characteristics are explained in depth. Another remarkable feature of the algorithm consists in that it works in Cartesian coordinates, bypassing the need to transform from the Cartesian to the polar domain, which, typically, is a numerically delicate and computationally onerous task. The proposed technique can become an effective tool for unsupervised estimation of roto-translations by means of implementations based on FFT algorithms.

Using saddle points for subpixel feature detection in camera calibration targets

The determination of reliable features with subpixel accuracy is an important requirement of any camera calibration algorithm. This paper offers a simple and computationally attractive method for extracting X-junctions with subpixel precision from images of calibration checkerboards by showing how the saddle points associated with them can be determined without any surface fitting required by standard feature detection algorithms.

Geometric calibration of digital cameras through multi-view rectification

This paper introduces a new and very effective method for high-precision geometric calibration of digital cameras. The internal and external geometry are estimated: (1) by extracting features with subpixel accuracy from various views of a planar calibration plate; and (2) by mapping these feature sets into the corresponding points of the undistorted and rectified image that would be generated by an ideal pinhole digital camera with the same focal length as the camera to calibrate but devoid of lens distortion and perspective warp. The rectification of the views is formulated as a nonlinear least-squares optimization problem where a quadratic cost function expressing the residual registration error has to be minimized. The views are first prealigned with the reference image by means of a simplified mathematical model. This initialization, together with the closed-form computation of the gradient of the cost function, allows the Levenberg-Marquardt algorithm employed to find its minimum to rapidly converge to the optimal solution. The performance of the new calibration algorithm is tested with a set of real images available on the Internet and discussed in the paper. Also, its accuracy is assessed by means of synthetic versions of the actual images generated with the estimated parameters.

A Frequency Domain Technique Based on Energy Radial Projections for Robust Estimation of Global 2D Affine Transformations

The contribution of this paper is twofold: (1) it provides a thorough analysis of the frequency domain relationships relating two affine-warped images and (2) based on a fundamental equation between energy radial projections, it presents an original algorithm for estimating the global 2D affine transformation between the two images. It is well known that operating in the frequency domain allows one to separate the estimate of the affine matrix, related to the magnitudes of the Fourier transforms of the two images, from the estimate of the translation vector, related to their phases. Exploiting this property, our algorithm consists of two main steps: (1) the affine matrix is first estimated by solving, with a coarse-to-fine strategy, a suitable minimization problem formulated upon the radial projections of the image energies, and (2) after compensation for the contribution of the affine matrix, the translation vector is then recovered by means of phase correlation. The proposed method is very robust against perspective distortion and, with moderate translational displacements, it may also work when the two images differ along their peripheral areas. Experimental evidence of these characteristics is reported and discussed. The algorithm can be efficiently implemented via FFT and well suits applications requiring unsupervised and/or quasi-real-time estimation of global motion that can be described with 2D affine transformations.

Frequency domain classification of cyclic and dihedral symmetries of finite 2-D patterns

This paper presents a very simple and effective algorithm for classifying cyclic and dihedral symmetries from images of finite two-dimensional patterns. It consists in an extension of a frequency domain algorithm proposed by the author for estimating two-dimensional rotation of rigid objects. Within this framework, the estimation of rotation is conveniently turned into the problem of detecting two orthogonal lines within the locus of the zero crossings of a certain function represented in orthogonal Cartesian coordinates. The main contribution of this paper is the use and interpretation of the ambiguities that arise in such a locus in the form of additional pairs of orthogonal lines when applied to symmetric patterns and the development of other algorithmic steps which allow a simple and fast discrimination between cyclic and dihedral symmetries. Unlike any other available method, this algorithm does not require any conversion from Cartesian to polar image representations. Besides classification reliability and consistency, observed through several dozen testing experiments, the nice features of this new method also include robustness to noise and ease of implementation with fast Fourier transform algorithms, which makes it amenable to almost real-time pattern classifications applications. Several examples, representative of the performance of the algorithm through extensive testing, are reported and discussed in the paper.

Filtering color images in the xyY color space

This paper presents a new approach to color filtering which operates on the representation of an image in the xyY color space. The filtering scheme, aided by the color mixing rule which applies to the 2D chromatic subspace spanned by the x and y coordinates, is shown to preserve the convexity of the chromatic information. Some examples of lowpass filtering with the new technique are reported.

Estimation of Two-Dimensional Affine Transformations Through Polar Curve Matching and Its Application to Image Mosaicking and Remote-Sensing Data Registration

This paper presents a new and effective method for estimating two-dimensional affine transformations and its application to image registration. The method is based on matching polar curves obtained from the radial projections of the image energies, defined as the squared magnitudes of their Fourier transforms. Such matching is formulated as a simple minimization problem whose optimal solution is found with the Levenberg-Marquardt algorithm. The analysis of affine transformations in the frequency domain exploits the well-known property whereby the translational displacement in this domain can be factored out and separately estimated through phase correlation after the four remaining degrees of freedom of the affine warping have been determined. Another important contribution of this paper, emphasized through one example of image mosaicking and one example of remote sensing image registration, consists in showing that affine motion can be accurately estimated by applying our algorithm to the shapes of macrofeatures extracted from the images to register. The excellent performance of the algorithm is also shown through a synthetic example of motion estimation and its comparison with another standard registration technique

Estimating affine transformations in the frequency domain

Estimation of 2D affine transformations is involved in several image processing and computer vision problems. Affine transformations are widely used for modelling relations between pairs of images. This paper presents a new frequency domain technique for estimating this kind of transformation. It consists of two main steps: (1) the affine matrix is first estimated by solving, with a coarse-to-fine strategy, a suitable nonlinear minimization problem formulated upon the radial projections of the image energies; (2) after compensating for the contribution of the affine matrix, the translation vector is then recovered by means of standard phase correlation. Experimental evidence of the effectiveness of this technique is reported and discussed.

A frequency domain technique for estimating rigid planar rotations

This work presents an original method for estimating planar rotations. The proposed technique operates in the frequency domain through the Fourier transform: hence, it uses all the information of the images and it can be efficiently implemented via FFT. The estimation of planar rotations lends itself to be treated in polar coordinates; however, the Cartesian to polar coordinates transformation turns out to be a delicate and heavy computational task. The proposed technique bypasses this problem by working in Cartesian coordinates directly and by exploiting the hermitian properties of the Fourier transform. Experimental evidence of the effectiveness and the robustness of the proposed method is reported.

Digital Pulse Shape Discrimination in Triple-Layer Phoswich Detectors Using Fuzzy Logic

In this paper, a new pulse shape discrimination algorithm for a triple-layer phoswich detector is implemented and tested. The three-layer detector which was used in this experiment was originally designed for simultaneous detection of beta particles and gamma rays in a mixed radiation field. The first two layers are specifically designed for beta particles and the third layer is designed for gamma-ray interaction. The pulse output of the photomultiplier is digitized and sent to the host computer for further processing. A de-noising algorithm based on the Wavelet Transform (WT) is implemented to reduce the effect of noise introduced by the noisy analog channel and by the photomultiplier tube. Three new timing features were extracted and given as input to a fuzzy interface system (FIS). The FIS output indicates to which scenario the input signal belongs. Compared to the non-fuzzy method which was initially implemented for this detector, the fuzzy algorithm shows a better performance in separating beta and gamma spectra, especially at high energies. Also, fewer pulses are rejected, due to classification as unknown pulses, and interaction in multiple layers is detected more efficiently.