Error Analysis for Image Inpainting

Image inpainting refers to restoring a damaged image with missing information. In recent years, there have been many developments on computational approaches to image inpainting problem [2, 4, 6, 9, 11–13, 27, 28]. While there are many effective algorithms available, there is still a lack of theoretical understanding on under what conditions these algorithms work well. In this paper, we take a step in this direction. We investigate an error bound for inpainting methods, by considering different image spaces such as smooth images, piecewise constant images and a particular kind of piecewise continuous images. Numerical results are presented to validate the theoretical error bounds. Tony F. Chan received the B.S. degree in engineering and the M.S. degree in aerospace engineering in 1973, from the California Institute of Technology, and the Ph.D. degree in computer science from Stanford University in 1978. He is Professor of Mathematics and currently also Dean of the division of Physical science at University of California, Los Angeles, where he has been a Professor since 1986. His research interests include mathematical and computational methods in image processing, multigrid, domain decomposition algorithms, iterative methods, Krylov subspace methods, and parallel algorithms. Sung Ha Kang received the Ph.D. degree in mathematics in 2002, from University of California, Los Angeles, and currently is Assistant Professor of Mathematics at University of Kentucky since 2002. Her research interests include mathematical and computational methods in image processing and computer vision.     

Total Variation Wavelet Inpainting

We consider the problem of filling in missing or damaged wavelet coefficients due to lossy image transmission or communication. The task is closely related to classical inpainting problems, but also remarkably differs in that the inpainting regions are in the wavelet domain. New challenges include that the resulting inpainting regions in the pixel domain are usually not geometrically well defined, as well as that degradation is often spatially inhomogeneous. We propose two related variational models to meet such challenges, which combine the total variation (TV) minimization technique with wavelet representations. The associated Euler-Lagrange equations lead to nonlinear partial differential equations (PDE’s) in the wavelet domain, and proper numerical algorithms and schemes are designed to handle their computation. The proposed models can have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients, including in the low frequencies. Existence and uniqueness of the optimal inpaintings are also carefully investigated. Research supported in part by grants ONR-N00014-03-1-0888, NSF DMS-9973341, DMS-0202565 and DMS-0410062, and NIH contract P 20 MH65166.     

Classification-based objective functions

Backpropagation, similar to most learning algorithms that can form complex decision surfaces, is prone to overfitting. This work presents classification-based objective functions, an approach to training artificial neural networks on classification problems. Classification-based learning attempts to guide the network directly to correct pattern classification rather than using common error minimization heuristics, such as sum-squared error (SSE) and cross-entropy (CE), that do not explicitly minimize classification error. CB1 is presented here as a novel objective function for learning classification problems. It seeks to directly minimize classification error by backpropagating error only on misclassified patterns from culprit output nodes. CB1 discourages weight saturation and overfitting and achieves higher accuracy on classification problems than optimizing SSE or CE. Experiments on a large OCR data set have shown CB1 to significantly increase generalization accuracy over SSE or CE optimization, from 97.86% and 98.10%, respectively, to 99.11%. Comparable results are achieved over several data sets from the UC Irvine Machine Learning Database Repository, with an average increase in accuracy from 90.7% and 91.3% using optimized SSE and CE networks, respectively, to 92.1% for CB1. Analysis indicates that CB1 performs a fundamentally different search of the feature space than optimizing SSE or CE and produces significantly different solutions. Editor: Risto Miikkulainen     

Microdeposition device interfacing capillary electrochromatography and microcolumn liquid chromatography with matrix-assisted laser desorption/ionization mass spectrometry

A sample deposition device has been constructed and optimized for interfacing CEC and capillary LC columns to MALDI mass spectrometry. For CEC analysis, the device is composed of an inlet buffer reservoir and an outlet buffer reservoir connected to a matrix reservoir through a connection sleeve. The matrix reservoir is connected to a deposition capillary via another connection sleeve. CEC eluent is transported to the matrix reservoir via a capillary that is connected to the deposition capillary by the connection sleeve inside the matrix reservoir. This connection sleeve also acts as a mixing chamber, allowing the CEC eluent to be mixed with matrix prior to deposition. Complex glycan mixtures can be separated by CEC using hydrophilic-phase monolithic columns, with capillary eluent being deposited on a standard MALDI plate along with a suitable matrix solution. Thousands of discrete, highly homogeneous dots can be generated for a subsequent mass spectrometric analysis. With minor modifications, this device is also applicable to capillary LC of peptides using gradient elution. In this configuration, the outlet of the LC column is connected to a deposition capillary inside a matrix reservoir through a connection sleeve that allows mixing of the LC effluent with an appropriate matrix. The device has been evaluated with the tryptic digests of proteins.     

Handwriting style classification

This paper describes an independent handwriting style classifier that has been designed to select the best recognizer for a given style of writing. For this purpose a definition of handwriting legibility has been defined and a method implemented that can predict this legibility. The technique consists of two phases. In the feature-extraction phase, a set of 36 features is extracted from the image contour. In the classification phase, two nonparametric classification techniques are applied to the extracted features in order to compare their effectiveness in classifying words into legible, illegible, and middle classes. In the first method, a multiple discriminant analysis (MDA) is used to transform the space of extracted features (36 dimensions) into an optimal discriminant space for a nearest mean based classifier. In the second method, a probabilistic neural network (PNN) based on the Bayes strategy and nonparametric estimation of probability density function is used. The experimental results show that the PNN method gives superior classification results when compared with the MDA method. For the legible, illegible, and middle handwriting the method provides 86.5% (legible/illegible), 65.5% (legible/middle), and 90.5% (middle/illegible) correct classification for two classes. For the three-class legibility classification the rate of correct classification is 67.33% using a PNN classifier.Received: 6 September 2002, Accepted: 19 September 2002, Published online: 6 June 2003     

Experimental and theoretical evidence for the magic angle in transmission electron energy loss spectroscopy

We present experimental measurements of the C K-ELNES of high temperature pyrolysed graphite and related crystalline materials as a function of collection angle and sample tilt. These results together with a corresponding theoretical analysis indicate that the so-called "magic angle" for EELS measurements of an anisotropic crystal such as graphite, where spectra are independent of sample orientation, is approximately two times the characteristic scattering angle. We briefly discuss the implications of this result for the experimental measurement of anisotropic structures, including interfaces, as well as for the detailed modelling of ELNES structures using advanced electronic structure calculations.     

High-speed path-length scanning with a multiple-pass cavity delay line

Techniques for high-speed delay scanning are important for low-coherence interferometry, optical coherence tomography, pump probe measurements, and other applications. We demonstrate a novel scanning delay line using a multiple-pass cavity. Differential delays are accumulated with each pass so that millimeter delays can be generated with tens of micrometer mirror displacements. With special design criteria, misalignment sensitivity can be dramatically reduced. The system is demonstrated to scan 6 m/s at 2-kHz repetition rates. Real-time optical coherence tomography imaging with 500 pixel images at four frames/s is performed. Using a Cr:forsterite laser source, we obtained axial image resolutions of 6 microm with 92-dB sensitivity.     

A comparison of the quantitative methods for the analysis of the platinum-containing anticancer drug [cis-[amminedichloro(2-methylpyridine)]platinum(II)] (ZD0473) by HPLC coupled to either a triple quadrupole mass spectrometer or an inductively coupled plasma mass spectrometer

The use of high performance liquid chromatography coupled with inductively coupled plasma mass spectrometry (HPLC-ICPMS) as means for the quantitative determination of ZD0473, a platinum anticancer drug, and its related biologically active "aqua" compounds in biofluid samples is described. The performance of the resulting HPLC-ICPMS method was compared with that of a conventional HPLC-triple quadrupole mass spectrometer-based (HPLC-MS/MS) system for properties such as limit of detection, linearity, and reproducibility using spiked samples. The methods were then applied to the determination of plasma ultrafitrate concentrations of ZD0473 in dog plasma samples obtained following intravenous and oral administration at 0.5 and 6 mg/kg, respectively. These experiments showed that both methods were capable of providing accurate and precise results but that the HPLC-ICPMS method had advantages of extended linear range and superior sensitivity, providing a limit of quantification of 0.1 ng/mL for ZD0473, as compared to 5 ng/mL using the current HPLC-MS/MS method. In addition, by using a single combined HPLC-ICPMS/MS/MS system, it was possible to determine the relative MS/MS response of the aqua compounds for the first time.     

Say it Like You Mean it: Priming for Structure in Caller Responses to a Spoken Dialog System

In this paper we report results of a study undertaken to evaluate the initial prompts of open prompt style call-routing applications. Specifically, we examined how placement and phrasing of examples in the initial query affected caller responses and routing success. We looked at the comparative effectiveness of placing examples before and after the initial query and of phrasing these examples such that they promoted either a succinct structure in the form of a keyword or phrase, or a more complex but natural structure in the form of a question or statement. Findings indicate that examples encouraging a more natural structure, when presented prior to the initial query, result in significantly improved routing performance. We discuss this result in the context of using initial prompts to prime for desired structure in caller responses.