Aykut Koç

Digital Computation of Linear Canonical Transforms

We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take ~ N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.

Efficient computation of quadratic-phase integrals in optics

We present a fast NlogN time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one need not choose N much larger than the space-bandwidth product of the signals, despite the highly oscillatory integral kernel. The only deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus the algorithm computes quadratic-phase integrals with a performance similar to that of the fast-Fourier-transform algorithm in computing the Fourier transform, in terms of both speed and accuracy.

Fast and accurate computation of two-dimensional non-separable quadratic-phase integrals.

We report a fast and accurate algorithm for numerical computation of two-dimensional non-separable linear canonical transforms (2D-NS-LCTs). Also known as quadratic-phase integrals, this class of integral transforms represents a broad class of optical systems including Fresnel propagation in free space, propagation in graded-index media, passage through thin lenses, and arbitrary concatenations of any number of these, including anamorphic/astigmatic/non-orthogonal cases. The general two-dimensional non-separable case poses several challenges which do not exist in the one-dimensional case and the separable two-dimensional case. The algorithm takes approximately N log N time, where N is the two-dimensional space-bandwidth product of the signal. Our method properly tracks and controls the space-bandwidth products in two dimensions, in order to achieve information theoretically sufficient, but not wastefully redundant, sampling required for the reconstruction of the underlying continuous functions at any stage of the algorithm. Additionally, we provide an alternative definition of general 2D-NS-LCTs that shows its kernel explicitly in terms of its ten parameters, and relate these parameters bidirectionally to conventional ABCD matrix parameters.

Fast and accurate algorithm for the computation of complex linear canonical transforms

A fast and accurate algorithm is developed for the numerical computation of the family of complex linear canonical transforms (CLCTs), which represent the input-output relationship of complex quadratic-phase systems. Allowing the linear canonical transform parameters to be complex numbers makes it possible to represent paraxial optical systems that involve complex parameters. These include lossy systems such as Gaussian apertures, Gaussian ducts, or complex graded-index media, as well as lossless thin lenses and sections of free space and any arbitrary combinations of them. Complex-ordered fractional Fourier transforms (CFRTs) are a special case of CLCTs, and therefore a fast and accurate algorithm to compute CFRTs is included as a special case of the presented algorithm. The algorithm is based on decomposition of an arbitrary CLCT matrix into real and complex chirp multiplications and Fourier transforms. The samples of the output are obtained from the samples of the input in approximately N log N time, where N is the number of input samples. A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.

Evaluation of Feature Channels for Correlation-Filter-Based Visual Object Tracking in Infrared Spectrum

Correlation filters for visual object tracking in visible imagery has been well-studied. Most of the correlation-filterbased methods use either raw image intensities or feature maps of gradient orientations or color channels. However, well-known features designed for visible spectrum may not be ideal for infrared object tracking, since infrared and visible spectra have dissimilar characteristics in general. We assess the performance of two state-of-the-art correlationfilter-based object tracking methods on Linköping Thermal InfraRed (LTIR) dataset of medium wave and longwave infrared videos, using deep convolutional neural networks (CNN) features as well as other traditional hand-crafted descriptors. The deep CNN features are trained on an infrared dataset consisting of 16K objects for a supervised classification task. The highest performance in terms of the overlap metric is achieved when these deep CNN features are utilized in a correlation-filter-based tracker.

Fast and accurate algorithms for quadratic phase integrals in optics and signal processing

The class of two-dimensional non-separable linear canonical transforms is the most general family of linear canonical transforms, which are important in both signal/image processing and optics. Application areas include noise filtering, image encryption, design and analysis of ABCD systems, etc. To facilitate these applications, one need to obtain a digital computation method and a fast algorithm to calculate the input-output relationships of these transforms. We derive an algorithm of NlogN time, N being the space-bandwidth product. The algorithm controls the space-bandwidth products, to achieve information theoretically sufficient, but not redundant, sampling required for the reconstruction of the underlying continuous functions.

MARVEL: A Large-Scale Image Dataset for Maritime Vessels

Fine-grained visual categorization has recently received great attention as the volumes of the labelled datasets for classification of specific objects, such as cars, bird species, and aircrafts, have been increasing. The collection of large datasets has helped vision based classification approaches and led to significant improvements in performances of the state-of-the-art methods. Visual classification of maritime vessels is another important task assisting naval security and surveillance applications. In this work, we introduce a large-scale image dataset for maritime vessels, consisting of 2 million user uploaded images and their attributes including vessel identity, type, photograph category and year of built, collected from a community website. We categorize the images into 109 vessel type classes and construct 26 superclasses by combining heavily populated classes with a semi-automatic clustering scheme. For the analysis of our dataset, extensive experiments have been performed, involving four potentially useful applications; vessel classification, verification, retrieval, and recognition. We report encouraging results for each application. The introduced dataset is publicly available.

Fast Algorithms for Digital Computation of Linear Canonical Transforms

Fast and accurate algorithms for digital computation of linear canonical transforms (LCTs) are discussed. Direct numerical integration takes O(N2) time, where N is the number of samples. Designing fast and accurate algorithms that take \(O(N\log N)\) time is of importance for practical utilization of LCTs. There are several approaches to designing fast algorithms. One approach is to decompose an arbitrary LCT into blocks, all of which have fast implementations, thus obtaining an overall fast algorithm. Another approach is to define a discrete LCT (DLCT), based on which a fast LCT (FLCT) is derived to efficiently compute LCTs. This strategy is similar to that employed for the Fourier transform, where one defines the discrete Fourier transform (DFT), which is then computed with the fast Fourier transform (FFT). A third, hybrid approach involves a DLCT but employs a decomposition-based method to compute it. Algorithms for two-dimensional and complex parametered LCTs are also discussed.

Fine-grained recognition of maritime vessels and land vehicles by deep feature embedding

Recent advances in large-scale image and video analysis have empowered the potential capabilities of visual surveillance systems. In particular, deep learning-based approaches bring in substantial benefits in solving certain computer vision problems such as fine-grained object recognition. Here, the authors mainly concentrate on classification and identification of maritime vessels and land vehicles, which are the key constituents of visual surveillance systems. Employing publicly available data sets for maritime vessels and land vehicles, the authors aim to improve visual recognition. Specifically, the authors focus on five tasks regarding visual recognition; coarse-grained classification, fine-grained classification, coarse-grained retrieval, fine-grained retrieval, and verification. To increase the performance in these tasks, the authors utilise a multi-task learning framework and present a novel loss function which simultaneously considers deep feature learning and classification by exploiting the available hierarchical labels of individual samples and the global statistics of distances between the data pairs. The authors observe that the proposed multi-task learning model improves the fine-grained recognition performance on MARVEL and Stanford Cars data sets, compared to training of a model targeting a single recognition task.

Measuring cross-lingual semantic similarity across European languages

This paper studies cross-lingual semantic similarity (CLSS) between five European languages (i.e. English, French, German, Spanish and Italian) via unsupervised word embeddings from a cross-lingual lexicon. The vocabulary in each language is projected onto a separate high-dimensional vector space, and these vector spaces are then compared using several different distance measures (i.e., correlation, cosine etc.) to measure their pairwise semantic similarities between these languages. A substantial degree of similarity is observed between the vector spaces learned from corpora of the European languages. Null hypothesis testing and bootstrap methods (by resampling without replacement) are utilized to verify the results.