Qing Wang

Bio: Qing Wang is an academic researcher from University of Freiburg. The author has contributed to research in topics: Fourier transform & Active contour model. The author has an hindex of 8, co-authored 10 publications receiving 224 citations.

Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates

Abstract: In this paper, polar and spherical Fourier analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. The proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures. The theory is compactly presented with an emphasis on the analogy to the normal Fourier transform. The relation between the polar or spherical Fourier transform and the normal Fourier transform is explored. As examples of applications, rotation-invariant descriptors based on polar and spherical Fourier coefficients are tested on pattern classification problems.

Fourier Analysis in Polar and Spherical Coordinates

Abstract: In this paper, polar and spherical Fourier Analysis are defined as the decomposition of a function in terms of eigenfunctions of the Laplacian with the eigenfunctions being separable in the corresponding coordinates. Each eigenfunction represents a basic pattern with the wavenumber indicating the scale. The proposed transforms provide an effective radial decomposition in addition to the well-known angular decomposition. The derivation of the basis functions is compactly presented with an emphasis on the analogy to the normal Fourier transform. The relation between the polar or spherical Fourier transform and normal Fourier transform is explored. Possible applications of the proposed transforms are discussed.

3D invariants with high robustness to local deformations for automated pollen recognition

Abstract: We present a new technique for the extraction of features from 3D volumetric data sets based on group integration. The features are invariant to translation, rotation and global radial deformations. They are robust to local arbitrary deformations and nonlinear gray value changes, but are still sensitive to fine structures. On a data set of 389 confocally scanned pollen from 26 species we get a precision/recall of 99.2% with a simple 1NN classifier. On volumetric transmitted light data sets of about 180,000 airborne particles, containing about 22,700 pollen grains from 33 species, recorded with a low-cost optic in a fully automated online pollen monitor the mean precision for allergenic pollen is 98.5% (recall: 86.5%) and for the other pollen 97.5% (recall: 83.4%).

2D/3D rotation-invariant detection using equivariant filters and kernel weighted mapping

Abstract: In many vision problems, rotation-invariant analysis is necessary or preferred. Popular solutions are mainly based on pose normalization or brute-force learning, neglecting the intrinsic properties of rotations. In this paper, we present a rotation invariant detection approach built on the equivariant filter framework, with a new model for learning the filtering behavior. The special properties of the harmonic basis, which is related to the irreducible representation of the rotation group, directly guarantees rotation invariance of the whole approach. The proposed kernel weighted mapping ensures high learning capability while respecting the invariance constraint. We demonstrate its performance on 2D object detection with in-plane rotations, and a 3D application on rotation-invariant landmark detection in microscopic volumetric data.

Fast and robust segmentation of spherical particles in volumetric data sets from brightfield microscopy

Abstract: In this article we present an approach for a precise segmentation of spherical particles in transmitted light image stacks. A main goal was its fast operation and a high robustness to occlusions and agglomerations of the particles. The system is based on a voting procedure that finds the centers and radii of the particles and a subsequent precise segmentation with an active contour approach. To meet the demands of an online pollenmonitor for high speed and low memory consumption a multi-scale approach was applied. The proposed techniques successfully segmented the pollen grains in a vast amount of different air samples (about 2.7TB of raw data). The results on one of the most cluttered samples are presented in this paper.

Advanced Calculus I

Abstract: WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Harmonic Networks: Deep Translation and Rotation Equivariance

Abstract: Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, returning a maximal response and orientation for every receptive field patch. H-Nets use a rich, parameter-efficient and fixed computational complexity representation, and we show that deep feature maps within the network encode complicated rotational invariants. We demonstrate that our layers are general enough to be used in conjunction with the latest architectures and techniques, such as deep supervision and batch normalization. We also achieve state-of-the-art classification on rotated-MNIST, and competitive results on other benchmark challenges.

Representing local structure using tensors II

Abstract: Estimation of local spatial structure has a long history and numerous analysis tools have been developed. A concept that is widely recognized as fundamental in the analysis is the structure tensor. However, precisely what it is taken to mean varies within the research community. We present a new method for structure tensor estimation which is a generalization of many of it's predecessors. The method uses filter sets having Fourier directional responses being monomials of the normalized frequency vector, one odd order sub-set and one even order sub-set. It is shown that such filter sets allow for a particularly simple way of attaining phase invariant, positive semi-definite, local structure tensor estimates. We continue to compare a number of known structure tensor algorithms by formulating them in monomial filter set terms. In conclusion we show how higher order tensors can be estimated using a generalization of the same simple formulation.

Harmonic Networks: Deep Translation and Rotation Equivariance

Abstract: Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, returning a maximal response and orientation for every receptive field patch. H-Nets use a rich, parameter-efficient and low computational complexity representation, and we show that deep feature maps within the network encode complicated rotational invariants. We demonstrate that our layers are general enough to be used in conjunction with the latest architectures and techniques, such as deep supervision and batch normalization. We also achieve state-of-the-art classification on rotated-MNIST, and competitive results on other benchmark challenges.

Autofluorescence of atmospheric bioaerosols – fluorescent biomolecules and potential interferences

Abstract: . Primary biological aerosol particles (PBAP) are an important subset of air particulate matter with a substantial contribution to the organic aerosol fraction and potentially strong effects on public health and climate. Recent progress has been made in PBAP quantification by utilizing real-time bioaerosol detectors based on the principle that specific organic molecules of biological origin such as proteins, coenzymes, cell wall compounds and pigments exhibit intrinsic fluorescence. The properties of many fluorophores have been well documented, but it is unclear which are most relevant for detection of atmospheric PBAP. The present study provides a systematic synthesis of literature data on potentially relevant biological fluorophores. We analyze and discuss their relative importance for the detection of fluorescent biological aerosol particles (FBAP) by online instrumentation for atmospheric measurements such as the ultraviolet aerodynamic particle sizer (UV-APS) or the wide issue bioaerosol sensor (WIBS). In addition, we provide new laboratory measurement data for selected compounds using bench-top fluorescence spectroscopy. Relevant biological materials were chosen for comparison with existing literature data and to fill in gaps of understanding. The excitation-emission matrices (EEM) exhibit pronounced peaks at excitation wavelengths of ~280 nm and ~360 nm, confirming the suitability of light sources used for online detection of FBAP. They also show, however, that valuable information is missed by instruments that do not record full emission spectra at multiple wavelengths of excitation, and co-occurrence of multiple fluorophores within a detected sample will likely confound detailed molecular analysis. Selected non-biological materials were also analyzed to assess their possible influence on FBAP detection and generally exhibit only low levels of background-corrected fluorescent emission. This study strengthens the hypothesis that ambient supermicron particle fluorescence in wavelength ranges used for most FBAP instruments is likely to be dominated by biological material and that such instrumentation is able to discriminate between FBAP and non-biological material in many situations. More detailed follow-up studies on single particle fluorescence are still required to reduce these uncertainties further, however.