Background

The invention of daguerreotype photography was made public at a meeting of the French Academy of Sciences in 1839. The first practical method to record the world in high fidelity, daguerreotype imagery transformed disciplines in both the arts and sciences [1]. The multistep process requires a Cu plate; (1) coated with Ag and polished to a mirror finish; (2) exposed to halogens; (3) exposed to light within the camera; (4) subjected to Hg vapors; (5) rinsed to remove remaining salts, and finally; (6) gilded with Au (Fig. 1). A physical model to explain the image contrast in daguerreotypes can be accounted for via diffuse reflectance of high density Hg-bearing nanoparticles in highlight regions, relative to specular reflectance in shadow regions that contain few image particles [2, 3]. Many daguerreotypes have survived >170 years in reasonably good condition. Other 19th century images suffer from a variety of degradation mechanisms, including; Ag sulfide tarnish films of differing thicknesses characterized by interference colors; Cu accretions; microbial filaments; and silicate detritus from unstable cover glass [4]. Efforts to study specific alteration mechanisms have been made to understand both chemical [5] and biological [6] processes.

Fig. 1
figure 1

Anatomy of a daguerreotype. Block diagram showing the microstratigraphic relationships within a daguerreotype: Cu plate; Ag thin film; zone of voids; Hg-bearing nanoparticles; and Au gilding [9]

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Examination of an entire daguerreotype plate, up to >350 cm2, 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 X-ray fluorescence spectrometry (µXRF) to reveal 2D elemental distributions of daguerreotype plates with X and Y dimensions on the scale of multi-centimeters. 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 x-ray 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 X-ray 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 trade-off 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 Haar-Fisz 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

Two daguerreotypes portraits were chosen for examination in this study: (1) a poorly preserved 31.75 mm/1¼ “round daguerreotype of two unknown males that was likely part of a 19th century pocket watch (Fig. 2, hereafter two boys); (2) a well-preserved sixth plate, 69.9 × 82.6 mm/2¾ × 3¼”, of an unknown young woman (Fig. 3, hereafter Woman Sitting). Specimens were imaged in an EDAX Eagle III µXRF. This system uses a polycapillary optic to focus the primary X-ray beam into an elliptical spot with a major axis diameter of approximately 50 µm. Samples were affixed to an XY raster stage. At each point, a full X-ray spectrum, 2048 channels at 10 eV per channel, is recorded and stored in a binary X-ray spectrum database. From the database, multiple software packages have been used to interrogate the data [13, 14]. Because the Eagle III system uses a Si(Li) detector, count rates were limited to approximately 20,000 counts/s. Thus, the full power of the X-ray tube was not exploited in order to prevent the detector from being paralyzed by dead times above 50 %. The X-ray data set for the Two Boys daguerreotype, was collected using a per-point integration time of 3 s, resulting in a total imaging time of approximately 116 h including instrument overhead. For the larger daguerreotype, Woman Sitting, an integration time of 1 s per point was used, resulting in a total acquisition time of approximately 64 h.

Fig. 2
figure 2

Poorly preserved daguerreotype. Round 31.75 mm, 1¼ inch, diameter daguerreotype portrait of two unknown boys. a Mosaic of negative images. Dotted outline marks the region covered by XRF imaging region. b Positive image of region highlighted by solid line in a

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Fig. 3
figure 3

Well preserved daguerreotype. Sixth plate daguerreotype 69.9 × 82.6 mm/2¾ × 3¼ inches portrait of an unknown woman. Red, blue, yellow, and gold in the dress bow, book binding, and tablecloth represent hand painted pigments unassociated with the photographic process. Dotted outline marks the region covered by XRF imaging

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Au + Hg Mα 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 X-ray compositional data set. Two algorithms were used to create the images in this study. The first algorithm executes the Haar-Fisz de-noising algorithm [16], while the second algorithm performs a multiple resolution analysis [17].

The Haar-Fisz transformation

The Haar-Fisz (H-F) 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. X-ray images are a two dimensional plot of the counts extracted from an X-ray 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 X-ray 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 trade-off, it is part of a well-established 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 Haar-Fisz 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 H-F transform is a two step process, beginning with a data transformation that noise-normalizes 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 near-perfect 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 Haar-Fisz 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 H-F 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 non-noisy 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 most useful X-ray image for depicting daguerreotype features is comprised of Au and Hg Mα X-rays (Fig. 4). Though convolved, the Au + Hg sum image offers an advantage as spectral deconvolution at each pixel would impose a data processing time penalty. The original, unprocessed images, as well as the processed data are shown in Figs. 5 and 6. Observing the differences between the raw and H-F transformed images reveals the subtle, but noticeable change in the images. The H-F image exhibits lower noise and the high contrast features of the image have not been significantly degraded. The details in the collars and in the ties of the Two Boys image have been preserved. In Woman Sitting, there are several facial features that are more apparent in the Haar-Fisz image, and there was excellent preservation of the details in the fingers and the pleats of the dress.

Fig. 4
figure 4

X-ray fluorescence spectrum of a tarnished daguerreotype. Convolved X-ray peaks in the vicinity of 2200 eV: Au (2123 eV) from the gilding; Hg (2195 eV) from image nanoparticles; and S (2308 eV) from Ag sulfide tarnish. The shaded spectral region of interest ROI outlined by dotted lines represents the sum of Au + Hg Mα X-ray lines. Deconvolved peaks: Au Mα (green); Hg Mα (blue); S Kα (dark green); and Ag Lα (cyan) shown beneath the convolved/sum spectrum (red)

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Fig. 5
figure 5

Multiple resolution analysis (MRA) processed-Two Boys. a Raw Au + Hg image. b Haar-Fisz transformed Au + Hg image. c MRA processed image. d Reflected light negative image

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Fig. 6
figure 6

Multiple resolution analysis (MRA) processed-Woman Sitting. a Raw Au + Hg image. b Haar-Fisz transformed Au + Hg image. c MRA processed image. d Reflected light image

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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).

It may appear that the spatial resolution of the compositional image has been degraded by executing the VST routines, yet this is not the case. To demonstrate that spatial fidelity of the image has not been lost, a line trace was performed across a high contrast feature within the Two Boys plate. The profile crosses multiple contrast boundaries of multiple midtones and highlight regions of the photograph. Figure 7 shows the results of the line trace for the raw and H-F transformed images. Linear measurements of daguerreotype features taken from either the raw data, or the transformed data, result in the same value. It should also be noted that the values from the collar were higher in the Haar-Fisz data. This is a common result of wavelet transformations, namely, an improvement in contrast of features in an image. There are other wavelet transformation methods that are designed to increase or improve contrast in images without increasing noise.

Fig. 7
figure 7

X-ray line profile across high contrast boundaries. Au + Hg X-ray counts as a function of distance along a one dimensional trace, where: The solid black line represents the raw/noisy data and the dashed blue line represents the Haar-Fisz transformed data. Double black arrows show that high contrast image features are identical in size regardless of whether the noisy-raw data, or Haar-Fisz transformed data, are used for measurement. Inset: Red arrow marks the location of the line profile on the Two Boys daguerreotype

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Discussion

Haar-Fisz VST image processing routines provide a noticeable improvement in noisy X-ray 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.

As a method of checking the conversion quality of the image, four regions on the Two Boys daguerreotype were selected for further analysis. These areas represent four gray scales ranges (Fig. 8). The rectangular region in each of the four areas contained approximately 1500 pixels. The mean and the variance of the pixels were calculated using Lispix [13]. These values were used to calculate the relative variance of each region, and those results are plotted in Fig. 8. The raw Au + Hg image, which is subject to Poisson counting statistics, should have a relative variance of approximately 1. The Haar-Fisz transformed data, no longer subject to the limitations of Poisson counting statistics, have a lower relative variance in those same regions.

Fig. 8
figure 8

Relative Variance of raw versus Haar-Fisz transformed images. The result of tracking the variance in four regions of the Two Boys image is shown. Inset: the Haar-Fisz transformed image is shown with yellow rectangles representing the areas sampled for computation. The data from the Haar-Fisz transformed image is shown as blue dots, and the data from the raw image is shown in magenta. Relative variance is represented by the variance divided by the mean

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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 non-sparse, 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 non-sparse 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 X-ray 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 state-of-the-art X-ray detectors, it is impractical to collect X-ray 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 X-ray images are available. Although the intensity of the X-ray signal was low, and the resulting Au + Hg daguerreotype images were of poor quality, Haar-Fisz 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 non-experts to take advantage of advancements in the field of digital image processing and analysis.