Optimizing compositional images of daguerreotype photographs using post processing methods
 Jeffrey M. Davis^{1} and
 Edward P. Vicenzi^{2}Email author
DOI: 10.1186/s4049401600807
© Davis and Vicenzi. 2016
Received: 22 October 2015
Accepted: 8 April 2016
Published: 27 May 2016
Abstract
Keywords
Early photography Image analysis Image processing Noise suppression Spectrum imaging XRF Xray imagingBackground
Examination of an entire daguerreotype plate, up to >350 cm^{2}, by optical imaging methods to document its condition is a useful endeavor [7]. Hyperspectral imaging of whole plates, particularly in the near infrared (NIR), has proven useful for discerning features obscured in visible wavelengths by Ag sulfide tarnish [8].
This study employs scanning microfocus Xray fluorescence spectrometry (µXRF) to reveal 2D elemental distributions of daguerreotype plates with X and Y dimensions on the scale of multicentimeters. Chemical documentation at the object scale complements optical imagery, and in many cases, identifies/confirms a degradation mechanism for any potential treatment. Because the information regarding the image and alteration products is encoded in the top ~100–200 nm of the plate [9, 10], and the primary xray signal penetrates many micrometers into the Ag coating and Cu bulk, the resultant chemical signal of interest is weak. Poor signal quality, on the order of less than 10 counts per second in the spectral region of interest (ROI), generally results in an unsatisfactorily noisy image [11]. In this case, the signal is dominated by the variance inherent to a Poisson distribution. The most commonly used strategy to reduce Poisson noise involves increasing the total number of counts in the signal. This is often accomplished by brute force data collection methods, such as; (1) increasing the power of the Xray source; or, (2) integrating the signal over a longer period of time [12]. However, because the photograph information is derived from a small mass, relative to the mass within the XRF activation volume of material, such data collection approaches are simply not efficient nor practical.
An alternative solution for improving image quality involves using image processing techniques, such as spatial binning of data over neighboring pixels, resulting in a smaller image with better statistics. Users of more advanced image processing software tools will also be familiar with techniques such as: (1) median filtering, where the statistics from eight neighboring pixels are used to reduce the noise of the image, or; (2) spline fitting, where a polynomial spline is fit to the image by rows or columns to reduce noise. These image processing techniques offer a useful tradeoff of spatial resolution for improved noise characteristics over a local neighborhood of pixels. The aim of this effort is to provide an example of a data processing approach that produces improved image information quality from raw µXRF imagery. This method relies on emerging concepts and data transformations being implemented in the signal processing community. Specifically, two methods will be considered: (1) The HaarFisz denoising transformation; and, (2) the Multiple Resolution Analysis method. The primary advantage of using these techniques is that they are able to improve the information quality of the data without sacrificing global spatial resolution. This is made possible through mathematical transformations that decouple the Poisson relationship between the intensity to noise ratio.
Methods
Au + Hg M_{α} sum images were transformed into a matrix in R, a freely available open source data analysis toolset [14], and processed using the {denoise.modwt.2d} function with the Haar wavelet selected as the analyzing wavelet. Numerous software packages, both open source and licensed software, are capable of performing the requisite image processing routines. The R package “waveslim” was selected owing to the simplicity of the analysis and the availability of suitable scripts [15]. Although the code is not speed or memory optimized, it can be used to process any Xray compositional data set. Two algorithms were used to create the images in this study. The first algorithm executes the HaarFisz denoising algorithm [16], while the second algorithm performs a multiple resolution analysis [17].
The HaarFisz transformation
The HaarFisz (HF) transform used here is a member of a class of transformations known as variance stabilization transforms (VST) [18]. These transforms are used to solve the problem at the root of all Poisson counting processes, specifically, that data variance scales with the number of counts. Xray images are a two dimensional plot of the counts extracted from an Xray region of interest, where high grayscale level pixels represent high counts/concentration of an element, and low greyscale level pixels represent correspondingly low counts/concentration of an element counts. The variance of the counts in each pixel in an Xray image is equal to the number of counts in that pixel, and the standard deviation is the square root of the number of counts. It follows that the variance and standard deviation increase with the number of counts. This may seem counterintuitive, given that higher count images, collected with a longer dwell time per point, have lower noise resulting in higher quality images. Our perception of image quality is based upon a visual approximation of the ratio of the noise to the signal. Thus, a point with 10,000 counts will have approximately 100 counts of noise, resulting in an n/s ratio of 0.01, or 1 %. For lower count images, such as the compositional images in this study, noise makes up a significantly larger fraction of the data. By decoupling the relationship between the variance and the number of counts, the primary constraint on image quality can be mitigated.
While this goal may seem unachievable without suffering an undesirable tradeoff, it is part of a wellestablished group of mathematical transformations used in the field of signal processing termed wavelet theory [19, 20]. Noise removal and image reconstruction methods are imperfect tools, but the procedures markedly improve image quality and reduce the contribution of Poisson noise. Ultimately, the goal of the HaarFisz transform is to change the relationship between the counts and the variance to that of a Gaussian system, rather than a Poisson system. “Gaussianized” noise is not subject to the variance constraint of a random Poisson system.
The HF transform is a two step process, beginning with a data transformation that noisenormalizes the counts. Once the data are transformed, a series of Haar wavelets are fit to the data. Haar wavelets can be efficiently implemented in software, and they are used to represent counts/intensity data, similar to a conventional statistical model. However, rather than a single function representing the data, numerous wavelets are fit to the data. These wavelets are sorted according to the noise component. The first wavelets fit to the data are smooth functions with almost no noise. Later wavelets contain successively more noise, and the final ones are almost exclusively noise. Adding all of the wavelets together results in a nearperfect reconstruction of the original image. However, the image can also be reconstructed by taking only a portion of the wavelets. In this study, only the first 75 % of the wavelets were used to reconstruct the image, and the result is an image with the noise components removed.
Multiple resolution analysis
The final step involves reprocessing the HaarFisz transformed data using the multiresolution analysis function (MRA). It is common in wavelet image analysis to use multiple algorithms, iterative algorithms and other combinations of image processing techniques. However, the process outlined above for the HF transform is very similar to the process used for the MRA. This function is an example of a discrete wavelet transformation routine whose goal is to decompose an image into a certain number of wavelet functions. The functions are sorted with regard to spatial resolution, from an entire image to a single pixel [17]. Once again, a portion of the resulting wavelets are used to reconstruct the image. The noisy components have resolutions of single pixels, while the nonnoisy components have resolutions of multiple pixels. With both transformations, it is important to remember that, at some point, the wavelets are smoothing out real data and variation. The selection of which range of wavelets to use is left to the user.
Results
The MRA solutions step has provided additional image contrast and feature improvement. Details within the collars and neck ties in the Two Boys are preserved, and several facial features, such as eyebrows and lip lines are more readily apparent. Sitting Woman MRA results are more subtle, however the visibility of the features in the hands and book are easier to discern. When compared to the reflected light image, it is clear the MRA processed Au + Hg image is not sensitive to surface imperfections and atmospheric alteration (Fig. 5c, d).
Discussion
HaarFisz VST image processing routines provide a noticeable improvement in noisy Xray imagery. While spatial binning of data results in the local loss of data at the several pixel level, image quality is improved without impacting the spatial resolution of the features in the daguerreotype (Fig. 7). However, it should be noted that this transform only improves spatial information quality. The spectral data from which these images are derived, remains unaltered. In the absence of performing the image transforms, one would be faced with increasingly long integration times for a data collection approach to achieve similar image quality to the results shown here. For example, an increase in dwell time by a factor of three would significantly increase the total frame time, and would only result in an improvement of approximately the square root of three in the noise of the image. For this reason the data processing approach was determined to be more desirable.
An important distinction should be made between wavelet based VSTs and other image processing and filtering techniques. Wavelet based methods, like those used in this study, are based upon the concept of sparsity. Noise, which is the random fluctuation of the signal, is a nonsparse, or ubiquitous, component of every image. Image features, such as the shapes and forms in daguerreotype photographs that are recognizable are termed, sparse features; capable of being represented by a series smooth functions. Unlike spline fitting, median filtering, or other digital filters, the purpose of the VST is to identify and discriminate between sparse and nonsparse features. As a result, they do not rely on local estimations of noise and signal, and as such, they improve the image without degrading spatial resolution of the image significantly. It should be noted that once transformed, the data can be passed through additional filters and image processing routines to further improve the information content. The two step process identified here can be implemented using a small number of lines of code (see Additional files 1, 2). Finally, the digitally processed compositional maps may be used to aid in the reconstruction of a heavily disfigured daguerreotypes given their insensitivity to Ag sulfide tarnish and other surface imperfections.
Conclusions
In cultural heritage research, the ability to collect large area images at high Xray count rate is often limited by the nature of the object of interest. The specimen may be large, rough, heterogeneous, and structurally complex. Additionally, an object may be available for study within a strictly defined time frame. These constraints may limit information quality and impose practical collection time limitations on the measurement. Even when employing stateoftheart Xray detectors, it is impractical to collect Xray image data over multiple days for most research groups given the demand on high cost instrumentation. The results of this study demonstrate that alternatives to longer integration times for improving the information quality of Xray images are available. Although the intensity of the Xray signal was low, and the resulting Au + Hg daguerreotype images were of poor quality, HaarFisz data transformations improved image quality without sacrificing spatial resolution. The approach presented here represents a specific wavelet theory solution one can employ among many such solutions. As the tools and algorithms used to perform these procedures mature, the implementation barrier will decrease accordingly, making it easier for nonexperts to take advantage of advancements in the field of digital image processing and analysis.
Abbreviations
 HF:

HaarFisz transform
 μXRF:

microfocus Xray fluorescence spectrometry
 MRA:

multiple resolution analysis
 ROI:

region of interest
 S/N, N/S:

signal to noise ratio, noise to signal
 VST:

variance stabilization transforms
 XRF:

Xray fluorescence spectrometry
Declarations
Authors’ contributions
JMD collected Xray image data, conducted all facets of image and data processing/statistical routines, and cowrote the paper. EPV provided the specimens for the study, established Xray imaging conditions with JMD, prepared figures, and cowrote the paper. Both authors read and approved the final manuscript.
Authors’ information
JMD is an application scientist with PNDetectors, GmbH and is an XRF spectroscopic imaging specialist. Before taking his current position he was a research engineer in the Materials Measurement Science Division at the National Institute of Standards and Technology in Gaithersburg, MD, USA. He is a director and member of the executive council of the Microanalysis Society. He has organized symposia on the topic of XRF imaging and analysis for the engineering and science communities. EPV is a research scientist who specializes in microanalysis at Smithsonian Institution’s Museum Conservation Institute and President of the International Union of Microbeam Analysis Societies.
Acknowledgements
The Two Boys daguerreotype was a gift to the Smithsonian Institution facilitated by Shannon Perich, Curator, Photographic History Collection. We acknowledge Melvin Wachowiak and E. Keats Webb for reflected light imaging support. Many thanks to the National Institute of Standards and Technology where the data for this effort were collected. We also wish to thank the Smithsonian Institution’s Museum Conservation Institute for generous support for this project.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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