Jan P. Allebach

Optimal image scaling using pixel classification

We introduce a new approach to optimal image scaling called resolution synthesis (RS). In RS, the pixel being interpolated is first classified in the context of a window of neighboring pixels; and then the corresponding high-resolution pixels are obtained by filtering with coefficients that depend upon the classification. RS is based on a stochastic model explicitly reflecting the fact that pixels falls into different classes such as edges of different orientation and smooth textures. We present a simple derivation to show that RS generates the minimum mean-squared error (MMSE) estimate of the high-resolution image, given the low-resolution image. The parameters that specify the stochastic model must be estimated beforehand in a training procedure that we have formulated as an instance of the well-known expectation-maximization (EM) algorithm. We demonstrate that the model parameters generated during the training may be used to obtain superior results even for input images that were not used during the training.

Scanner identification using sensor pattern noise

Digital images can be captured or generated by a variety of sources including digital cameras and scanners. In many cases it is important to be able to determine the source of a digital image. This paper presents methods for authenticating images that have been acquired using flatbed desktop scanners. The method is based on using the pattern noise of the imaging sensor as a fingerprint for the scanner, similar to methods that have been reported for identifying digital cameras. To identify the source scanner of an image a reference pattern is estimated for each scanner and is treated as a unique fingerprint of the scanner. An anisotropic local polynomial estimator is used for obtaining the reference patterns. To further improve the classification accuracy a feature vector based approach using an SVM classifier is used to classify the pattern noise. This feature vector based approach is shown to achieve a high classification accuracy.

A dual interpretation for direct binary search and its implications for tone reproduction and texture quality

The direct binary search (DBS) algorithm employs a search heuristic to minimize the mean-squared perceptually filtered error between the halftone and continuous-tone original images. Based on an efficient method for evaluating the effect on the mean squared error of trial changes to the halftone image, we show that DBS also minimizes in a pointwise sense the absolute error under the same visual model, but at twice the viewing distance associated with the mean-squared error metric. This dual interpretation sheds light on the convergence properties of the algorithm, and clearly explains the tone bias that has long been observed with halftoning algorithms of this type. It also demonstrates how tone bias and texture quality are linked via the scale parameter, the product of printer resolution and viewing distance. Finally, we show how the tone bias can be eliminated by tone-correcting the continuous-tone image prior to halftoning it.

Analysis of error in reconstruction of two-dimensional signals from irregularly spaced samples

We consider the problem of estimating a band-limited two-dimensional (2-D) signal based on a finite set of irregularly spaced samples. We derive the minimum mean-squared error estimator of the form of a sum of weighted interpolating functions that are identical in shape but are centered at the irregularly spaced sample points, and show that this estimator is identical to the minimum energy band-limited interpolator that has been previously obtained by others. The relation between the mean-squared error and the set of irregularly spaced sampling points is studied using the minimax principle. The maximum of the mean-squared error over a class of signals is minimized by proper choice of the set of sampling points. Three criteria for evaluating the performance of the sampling point set are derived. From a candidate group of sets of irregularly spaced sampling points, these criteria may be used to select that point set which is optimal for recovery over a class of signals.

Quantization and multilevel halftoning of color images for near-original image quality

Algorithms are investigated for the printing or display of color images at near-original image quality with a minimum number of output colors. Each algorithm consists of a quantizer that is used possibly in conjunction with halftoning. We consider both image-independent and image-dependent quantizers implemented in RGB or in the uniform color space L*u*υ*. The halftoning techniques that we use are multilevel extensions of error diffusion and ordered dither. Image quality resulting from the use of these algorithms is measured by subjective evaluation.

New results on reconstruction of continuous-tone from halftone

Two iterative methods are used to reconstruct a continuous-tone image from its halftone: successive approximation and projection onto convex sets. The halftone image is assumed to be generated by thresholding with an unknown screen function which is estimated from the halftone image in the first stage of the reconstruction process. The screen function is an integral part of both iterative reconstruction methods. The other key element is a constraint on the bandwidth of the reconstructed image. Relaxing this constraint during the course of the iterations not only reduces the RMS error after each iteration but also achieves a relatively sharp full-band reconstruction at the end.<<ETX>>

Halftoning via direct binary search using analytical and stochastic printer models

We incorporate models for printer dot interactions within the iterative direct binary search (DBS) halftoning algorithm. Monochrome electro-photographic printers are considered. Both analytical and stochastic models are studied. In the analytical model it is assumed that the printer can generate a circular spot with constant absorptance at each printer addressable location, whereas the stochastic model is based on microscopic absorptance and variance measurements. We also present an efficient strategy for evaluating the change in computational cost as the search progresses. With our scheme, updating the change in error only involves a few fetches from two look-up-tables and some scalar multiplications and additions. Experimental results are provided that show that DBS with an appropriate model for printer dot interactions yields enhanced detail rendition, and improved tonal gradation in shadow areas.

Methodology for designing image similarity metrics based on human visual system models

In this paper we present an image similarity metric for content-based image database search. The similarity metric is based on a multiscale model of the human visual system. This multiscale model includes channels which account for perceptual phenomena such as color, contrast, color-contrast and orientation selectivity. From these channels, we extract features and then form an aggregate measure of similarity using a weighted linear combination of the feature differences. The choice of features and weights is made to maximize the consistency with similarity ratings made by human subjects. In particular, we use a visual test to collect experimental image matching data. We then define a cost function relating the distances computed by the metric to the choices made by the human subject. The results indicate that features corresponding to contrast, color-contrast and orientation can significantly improve search performance. Furthermore, the systematic optimization and evaluation strategy using the visual test is a general tool for designing and evaluating image similarity metrics.

Efficient model based halftoning using direct binary search

The direct binary search (DBS) algorithm is an iterative method which minimizes a metric of error between the grayscale original and halftone image. This is accomplished by adjusting an initial halftone until a local minimum of the metric is achieved at each pixel. The metric incorporates a model for the human visual system (HVS). In general, the DBS time complexity and halftone quality depend on three factors: the HVS model parameters, the choice of initial halftone, and the search strategy used to update the halftone. Despite the complexity of the DBS algorithm, it can be implemented with surprising efficiency. We demonstrate how the algorithm exploits the model for the HVS to efficiently yield very high quality halftones.

Sequential linear interpolation of multidimensional functions

We introduce a new approach that we call sequential linear interpolation (SLI) for approximating multidimensional nonlinear functions. The SLI is a partially separable grid structure that allows us to allocate more grid points to the regions where the function to be interpolated is more nonlinear. This approach reduces the mean squared error (MSE) between the original and approximated function while retaining much of the computational advantage of the conventional uniform grid interpolation. To obtain the optimal grid point placement for the SLI structure, we appeal to an asymptotic analysis similar to the asymptotic vector quantization (VQ) theory. In the asymptotic analysis, we assume that the number of interpolation grid points is large and the function to be interpolated is smooth. Closed form expressions for the MSE of the interpolation are obtained from the asymptotic analysis. These expressions are used to guide us in designing the optimal SLI structure. For cases where the assumptions underlying the asymptotic theory are not satisfied, we develop a postprocessing technique to improve the MSE performance of the SLI structure. The SLI technique is applied to the problem of color printer characterization where a highly nonlinear multidimensional function must be efficiently approximated. Our experimental results show that the appropriately designed SLI structure can greatly improve the MSE performance over the conventional uniform grid.