Björn Labitzke

High-quality computational imaging through simple lenses

Modern imaging optics are highly complex systems consisting of up to two dozen individual optical elements. This complexity is required in order to compensate for the geometric and chromatic aberrations of a single lens, including geometric distortion, field curvature, wavelength-dependent blur, and color fringing. In this article, we propose a set of computational photography techniques that remove these artifacts, and thus allow for postcapture correction of images captured through uncompensated, simple optics which are lighter and significantly less expensive. Specifically, we estimate per-channel, spatially varying point spread functions, and perform nonblind deconvolution with a novel cross-channel term that is designed to specifically eliminate color fringing.

Generic visual analysis for multi- and hyperspectral image data

Multi- and hyperspectral imaging and data analysis has been investigated in the last decades in the context of various fields of application like remote sensing or microscopic spectroscopy. However, recent developments in sensor technology and a growing number of application areas require a more generic view on data analysis, that clearly expands the current, domain-specific approaches. In this context, we address the problem of interactive exploration of multi- and hyperspectral data, consisting of (semi-)automatic data analysis and scientific visualization in a comprehensive fashion. In this paper, we propose an approach that enables a generic interactive exploration and easy segmentation of multi- and hyperspectral data, based on characterizing spectra of an individual dataset, the so-called endmembers. Using the concepts of existing endmember extraction algorithms, we derive a visual analysis system, where the characteristic spectra initially identified serve as input to interactively tailor a problem-specific visual analysis by means of visual exploration. An optional outlier detection improves the robustness of the endmember detection and analysis. An adequate system feedback of the costly unmixing procedure for the spectral data with respect to the current set of endmembers is ensured by a novel technique for progressive unmixing and view update which is applied at user modification. The progressive unmixing is based on an efficient prediction scheme applied to previous unmixing results. We present a detailed evaluation of our system in terms of confocal Raman microscopy, common multispectral imaging and remote sensing.

Efficient, robust, and scale-invariant decomposition of Raman spectra

Raman spectroscopy is used to identify unknown constituent minerals and their abundances since Raman spectra convey characteristic information about the samples chemical structure. We present a novel method to identify constituting pure minerals in a mixture by comparing the measured Raman spectra with a reference database. Our method comprises of two major components: A novel scale-invariant spectral matching technique, that allows to compare measured spectra with the reference spectra from the database even when the band intensities are not directly comparable and an iterative unmixing scheme to decompose a measured spectrum into its constituent minerals and compute their abundances.

Partial generalized correlation for hyperspectral data

A variational approach is proposed for the unsupervised assessment of attribute variability of high-dimensional data given a differentiable similarity measure. The key question addressed is how much each data attribute contributes to an optimum transformation of vectors for reaching maximum similarity. This question is formalized and solved in a mathematically rigorous optimization framework for each data pair of interest. Trivially, for the Euclidean metric minimization to zero distance induces highest vector similarity, but in case of the linear Pearson correlation measure the highest similarity of one is desired. During optimization the not necessarily symmetric trajectories between two vectors are recorded and analyzed in terms of attribute changes and line integral. The proposed formalism allows to assess partial covariance and correlation characteristics of data attributes for vectors being compared by any differentiable similarity measure. Its potential for generating alternative and localized views such as for contrast enhancement is demonstrated for hyperspectral images from the remote sensing domain.

Computational methods for aberration correction in simple lens imaging

The complexity of camera optics has greatly increased in recent decades. The lenses of modern single-lens reflex (SLR) cameras may contain a dozen or more individual lens elements, which are used to optimize the light efficiency of optical systems while minimizing the imperfections inherent in them. Geometric distortions, chromatic aberrations, and spherical aberrations are prevalent in simple lens systems and cause blurring and loss of detail. Unfortunately, complex optical designs come at a significant cost and weight. Instead of developing ever more complex optics, we propose1 an alternative approach using much simpler optics of the type used for hundreds of years,2 while correcting for the ensuing aberrations computationally. Although using computational methods for aberration correction has a long history,3–7 these methods are most effective in the removal of residual aberrations found in already well-corrected optical systems. A combination of large-aperture simple lens optics with modern high-resolution image sensors can result in very large wavelength-dependent blur kernels (i.e., point spread functions or PSFs: the response of an imaging system to a point source), with disk-shaped supports of 50–100 pixels diameter (see Figure 1). Such large PSFs destroy high-frequency image information, which cannot be recovered using existing methods. The fundamental insight of our work is that the chromatic part of the lens aberration (which occurs when colors are not focused to the same convergence point) can be used to our advantage, since the wavelength dependence of the blur means that different spatial frequencies are preserved in different color channels. Moreover, combining information from different color channels and enforcing consistency of edges (and similar image features) Figure 1. Calibrated point spread functions (PSFs) for two simple lenses, for different regions on the image sensor. (a) PSF of a 100mm biconvex lens at f/2.0. (b) PSF of a 130mm plano-convex lens at f/4.5.

Efficient and accurate linear spectral unmixing

The techniques of multi- and hyperspectral imaging have gained a growing attention in recent years. This is mostly due to their potential to provide rich information that can be used to improve material classification or product quality assessment. Linear spectral unmixing is a standard approach in hyperspectral data analysis. Based on the assumption that a spectral dataset can be expressed as a linear combination of constituent spectra, it is an important task to estimate the necessary coefficients. In the case that non-negativity of the coefficients is enforced, the calculation of the coefficients can be very time consuming. In this paper, we propose an GPU-based approach that efficiently and accurately computes the coefficients for linear spectral unmixing. Our approach is based on the orthogonal subspace projection technique and further can be combined with the image space reconstruction algorithm (ISRA) in order to improve the results in terms of accuracy and performance. We present detailed results of our proposed approach in comparison to ISRA for the domain of remote sensing.

Radviz-based visual analysis of multispectral images

The technique of multispectral imaging has gained growing attention in recent years. This is mostly due to the potential to provide rich information that can be used to improve material classification or product quality assessment. Due to the complex nature of the corresponding datasets, processing tools are needed to gain insights into the data. In this paper, we propose an analysis tool to assist a user with the interactive evaluation of multispectral images. The aim of the approach is to provide easier access to the wealth of information and to obtain a segmented multispectral image. Multivariate radial- and image-based visualizations, are meaningfully combined by linked views to find a proper segmentation in a semi-automatic way. The linked views are complemented by a novel evaluation view that allows the evaluation and the refinement of the segmentation, if necessary. We show usage examples of our proposed processing approach for multispectral scene data.