Can image analysis provide information useful in chemistry?

JOURNAL OF CHEMOMETRICS, VOL. 3, 419-429 (1989)

CAN IMAGE ANALYSIS PROVIDE INFORMATION USEFUL IN CHEMISTRY?

PAUL GELADI Research Group for Chemometrics, Umed University, S-901 87 UmeB, Sweden

A N D

KIM ESBENSEN Norwegian Computing Center, PB 114 Blindern, N-0314 Oslo 3, Norway

SUMMARY

Images can contain chemical information and many chemical methods can generate image data. For an efficient extraction of chemical data from images, data analysis techniques are necessary. It is a great advantage to be able to work on multivariate images. Many imaging techniques allow the extraction of chemical information. Inorganic analytical chemistry seems to have the longest tradition here, but organic chemistry and biochemistry may soon be catching up. Also large data arrays from non-imaging techniques can be combined with image analysis in a useful way, provided certain conditions are fulfilled.

KEY WORDS Image analysis Chemical imaging Multivariate image analysis Image analysis for non-imaging techniques

INTRODUCTION

Many techniques in chemistry are capable of generating images. Observation using the human eye is also one of the oldest and most powerful methods of scientific investigation. Visual observation has contributed to the development of imaging tools. In many sciences optical and electron microscopy have a long tradition, and learning to use them belongs to the classical scientific education, for example, in medicine, biology and geology and of course also in chemistry. The 1988 review issue of Analytical Chemistry shows evidence that chemistry and imaging are related.’.’

The modern age of computing has changed thinking in many areas of science. Also the collection and treatment of images has been computeri~ed.*’~ This is only a recent development and much still remains to be done. The first uses of computerized image treatment were mainly focused on correction of errors. These errors were caused by projection through a lens or by electronic or optical transmission. To this can be added errors caused by sources and detectors. Later there was a shift of attention to analysis: extracting usefuf information. Techniques of segmentation, often combined with filtering, were used for discriminating objects from a background and measuring the objects. Only in the last five years has one started to look at multivariate images. This trend opens the way for some exciting possibilities in the chemical use of images. For chemical classification and

088&9383/89/0204 19-1 1 $05.50 @ 1989 by John Wiley & Sons, Ltd.

Received 5 July I988 Revised 14 September 1988

420 P. GELADI AND K . ESBENSEN

concentration determination, multivariate data in each pixel are an absolute requirement in any non-trivial situation.

This paper includes sections on the definition, limitations, chemical uses and multivariate data analysis of images and a section on using non-imaging techniques. It is meant as a tutorial introduction to more papers on some of these subjects to appear in the future. Because of the tutorial nature, a fairly extensive reference list has been included.

DEFINITION O F IMAGES

There is a multitude of definitions of an image. Images have certain properties that make them images. The definition of these properties is more involved with perception psychology than with technical issues. This makes objective definitions difficult. A subjective list of useful properties is:

1. Each object (pixel) in an image has at least two indices. 2. An inter-object distance can be formulated. Distances can be calculated from the index

pairs (triplets, . . . ). 3. The minimal size is about 64x64. 4. There is at least some spatial autocorrelation. Property 1 has to do with the physiology of the human eye and the traditions of art: an image

is at least two-dimensional. Limitations of book reproductions, the photographic process and television screens make the majority of everyday images two-dimensional. Three-dimensional images can be and are obtained in tomography, both x-ray and NMR. One could also mention holography and stereology. Three-dimensional image analysis is slowly making its entry into the technology’&” and many commercial companies are secretly preparing 3D software prototypes, allowing projection or slicing from 3D to a 2D screen, where different projection and slicing angles can be requested.

Of importance is the case of higher-dimensional images: four-dimensional, five- dimensional, etc. Such images may be thought of in the present context, for example, as three-dimensional imaging of the time evolution of a scene (four-dimensional) or excitation-emission fluorescence analysis of voxels (volume elements) in a sample (five-dimensional). Under certain circumstances these multiway data arrays could be considered as 4D or 5D images respectively.2o Image analysis techniques for these should be developed.

Property 2 is one that makes images different from some other arrays, where this distance does not have a strict geometrical meaning.

Property 3 is purely psychological. This size was proposed as something subjective: 64x64 images are limit cases. Anything smaller does not cause a visual stimulus, while anything larger usually does. There is of course also a dependence on the scene presented. Sizes that are often used are 512x512 and 256x256. This has to do with screen sizes and TV camera resolution. In the future larger sizes such as 1024x1024 or 2048x2048 may become the standard.

Property 4 is probably the most important one but is also the most difficult to explain. It contains concepts such as context, structure and texture that all can be defined by a special type of spatial autocorrelation, but where the autocorrelation function possesses singularities.

SOME LIMITATIONS OF IMAGES

The human observer sometimes gets the impression that an image of a scene is the scene itself. This is not at all true. A digitized image is a projection-a representation of the scene.

IMAGE ANALYSIS IN CIIEMISTRY 421

Imagine projecting a scene from nature (a landscape) through a lens and onto a

1. The projection is geometrically non-linear. Most methods of imaging create projections that are best in the centre and worst in the corners. Lines and angles are often distorted away from the centre of an image.

2. Spatial resolution is lost. Many image analysis systems provide zoom utilities, but large zoom factors cannot provide more information than down to pixel size. Photographic images only show randomly ordered silver grains when extreme enlargements are used.

3. Wavelength or energy resolution is scrambled or lost. Most detectors are wide-band with a certain sensitivity curve. Filters or monochromators are necessary for extracting information in smaller bands.

4. Dynamic range is compressed. Extreme intensity ranges in nature are compressed to about 250 by photographic film and to a maximum of 40 on paper copies. The intensity range in question is often termed the ‘dynamic range’. Video cameras only have a dynamic range of about 30. Also the resolution between minimum and maximum intensity is often limited. Photomultipliers have a rather large intensity range and good resolution but are expensive and slow imagers.

5. Depth resolution is lost. In the best case it is substituted by perspective. For tomographic techniques the depth information is retained, but at the expense of enormous calculations and storage requirements.

6. There is an ‘edge’, a geometrical limit to the image. For microscopy or remote sensing the useful information is inside the edges. For tomographic techniques the body under study fills only part of the image and many pixels or voxels just represent empty space.

Most of the problems encountered in univariate image analysis have to do with single limitations from the list above or with combinations of them.

Many proposed algorithms become much larger and very much slower because of these limitations. This is because many methods operate on neighbourhoods in an image. Close to the edge these neighbourhoods become incomplete. A good example is the correction for the missing data outside the edge in 2D Fourier analysis.

It is a good habit to take extreme care in avoiding problems caused by limitations such as those mentioned above when digitizing an image and not to leave too much error correction to the electronics and computing part.

The corrections for the above mentioned limitations are discussed in the image analysis They are of little consequence to the chemical (or other) interpretation of an

image or a group of images. In the rest of this paper it is assumed that all images used have been collected and corrected in an optimal way.

photographic plate or a videotube. The following limitations occur:

CHEMICAL USES OF IMAGES

The relation between an image and the chemical/physical properties of the object under study is dependent on the spectral behaviour of the imaging system. An image, e.g. a transmission image from optical microscopy consists of intensity values. These can easily be transformed to transmissions or absorbances. This immediately reminds one of spectrometric quantitation, only instead of measuring absorbance averaged over one cuvette length there are now 262 144 small cuvettes in a 512x512 pixel image.

This simple comparison is meaningful, but lots of technical problems prevent its problem-free usage. Irregular illumination intensity, loss of contrast, low intensity resolution


of the detector and geometrical blurring are just a small collection of potential problems making the representation of intensity images as arrays of small cuvettes far from trivial.

Besides the above mentioned physical limitations, there are also chemical problems when many chemical substances are present in the sample, leading to matrix effects, interferences, etc. There is no way of relating concentration with intensity (transmission, absorbance) when more than one absorbing constituent is present and their spectra overlap. This leads to the need for multivariate measurement and multivariate calibration, also in chemical image analysis.

The hypothetical example given above was only for transmission of an ideal sample. Extra complications arise when optical dispersion is present or when reflectance measurements are made, or a combination of both. Also these complications can be dealt with when many wavelengths-a spectrum-are measured.

The optical variable 'wavelength' can be replaced by others such as electron energy, pulse sequence or ultrasound wavelength when non-optical imaging techniques are used. A summary of possible variables and their uses is given in Table 1. Also the physical disturbances do not always have to be of an optical nature.

Table 1. Variables used for creating univariate or, multivariate images

Variable Used in

Wave1ength:visible + UV

Wave1ength:infrared

Wave1ength:x-ray

Wavelengthxadio Electron energy mle

Pulse sequence or contrast chemical Ultrasound frequency

Remote sensing2' Light microscopy Fluorescence m i c r o ~ c o p y ~ ~ - ~ ~ Remote sensing2' Macroscopy ~ i c r o s c o p y ~ ~ X-ray tomography X-ray m i c r o ~ c o p y ~ ~ . ~ ~ Electron microscopy2 P1XE28 Radar remote sensing Electron microscopy2%3' SIMS32-38

NMR

Ultrasound imaging4u6

In general, when a number of chemical constituents are to be measured quantitatively in a complex sample having physical interferences, a large enough number of variables should be measured for each pixel to allow for the detection and correction of physical disturbances and for quantitation of each constituent.

An overview of potential chemical uses of imaging techniques is given in Table 2. Chemical analysis leading to concentrations is not always the goal of chemical image

analysis. Sometimes the liquid and solid phases in an image are sufficiently chemically different to allow a classification of, for example, histological type. This is typical for NMR

IMAGE ANALYSIS IN CHEMISTRY 423

Table 2. Chemical information to be gained from images

Type of imaging Chemical information

Radiology

Microscopy

NMR imaging

SIMS + electron microscopy Satellite imaging (remote sensing)

Ultrasound imaging

Concentration of radioactive elements Concentrations of absorbing substances Histochemical classification Concentration of active or contrast substances Histochemical classification Concentration of elements Inorganic chemistry Presence of water Organichnorganic land cover Mineralization fingerprints Agricultural usage Physical properties Histochemical classification

imaging,”’ where tissues have to be differentiated according to their lipid, water, . . . content, etc.

Histochemical classification of multivariate images is the first step towards chemical image analysis. In many cases it is all that is needed to solve a problem.

An interesting but difficult technique for histological imaging is the use of ultrasound waves43 in medical echography and the related acoustic microscopy.-6 It is expected that the use of many wavelengths can contribute to better histochemical classifications in these areas.

Inorganic analytical chemistry has a large advantage over organic chemistry when it comes to chemical imaging.47 Techniques like electron microscopy with x-ray detection (and all kinds of electron energy detection), secondary ion mass spectrometry (SIMS), proton-induced x-ray emission (PIXE) and gamma radiology of radioactive elements are element-specific and greylevel images of (approximate) element concentrations can be easily produced. In organic chemistry and biochemistry there are more subtle differences between the different interesting chemical constituents. Techniques like fluorescence microscopy, near-infrared and infrared imaging and of course NMR imaging can be improved to make organic chemical analysis of images more specific and accurate.

DATA ANALYSIS OF MULTIVARIATE IMAGES

The traditional view of images is as greylevel (intensity) images. The intensities measured are for a certain set of instrument parameters, e.g. a certain wavelength in microscopy. But one could also also measure the integral over a wide-band filter. Since images contain so much information, the goal of scientists has almost always been to select the parameter or set of parameters that gives the ‘best’ image. Only recently has one started thinking of multivariate


images. The field where this has made most impact is remote sensing2'-satellite imaging-but here what one mostly sees is image processing instead of image analysis.

It has been found very useful to represent each pixel in an image not by a single greyvalue but by a vector containing values for a suite of different variables. Multivariate modelling and multivariate regression on the multivariate images are necessary for chemical quantitation.

Figure 1 shows a representation of a digitized image as a square. The information consists of a greylevel in each pixel. Under the right circumstances this greylevel information can be interpreted chemically as concentrations. This is used, for example, in radiometry for radioactive objects. When only one well known chemical element is radioactive, the greylevel image is sufficient for quantitation. When the same image is measured for different wavelengths, a multivariate image exists. Each pixel is now a vector of spectral intensities. The chemical information in the multivariate image is in the spectral vectors. The geometrical information-context , structure and texture informatiowresides in the neighbourhood relationships. This information can be different for each wavelength. There are more efficient techniques than looking at each image in the stack separately. It is here that multivariate image analysis (MIA) comes in.

5 1 2 n GREYUDLUES

GEOGRBPHICAL. STRUCTURE, TEXTURE, CONTEXT INFORNBTIOH

SPECTRRL INFORMRTION GREYUBLUES FOR MANY

5 1 2 (-0 WRUELENGTHS

Q

Figure 1 . A greyvalue (intensity) image and a multivariate image measured for Q variables (often wavelengths). A popular size is 512x512. The geometrical (geographical) information is seen when looking from above, while the

chemical/physical information is available when looking from the side

The techniques for multivariate data analysis can with some modification be used for multivariate image analysis. Methods like principal component analysis4749 and regression") can be used on multivariate images. A special strategy for multivariate image analysis is required for extracting the information." An advantage is that most of the calculated results are images in themselves and can be examined visually. Figure 2 shows how a multivariate image can be projected into score images. The result is also a residual. Many interesting statistics can be calculated on this residual.

Models such as that in Figure 2 can provide a lot of useful information. Scatter plots of scores and of loadings can be made. Score plots show distances between objects (here pixels) in multivariate pace.^^,'' Loading plots allow one to investigate the importance of variables for the model. From the multivariate residual image, residual statistics such as sum of squares,


variance and standard deviation for each pixel can be calculated and shown as images. The model in Figure 2 is not necessarily made for a whole image, but classes can be selected for constructing local models. A well-chosen segmentation on, for example, the standard deviation image can provide a binary class membership image where all in-class pixels are white and all out-of-class pixels are black. The residual image stack itself can also be studied in the raw form.

An even more interesting situation than that in Figure 2 exists when external information is available for some or all pixels in the multivariate image. A multivariate regression model can be built up between the vectors in the image and the external data. This external data could be geological 'ground truth' for parts of a satellite image or medical knowledge for parts of an MRI image. Because of the expected collinearites between the variables of a multivariate image, the regression model has to be built with orthogonal latent variables. This can be done

512

512

P

512

P

J,

Figure 2. A multivariate image of Q variables can be represented as (projected into), for example three principal component images:T,. T2 and T,. A multivariate residual 9 can be derived on which the 'fit' to a model can bc estimated. A great advantage is that all results of operations can be visuatly interpreted as images (boldface

underlined characters arc used for rnultiway arrays)


+ tilode1 Inage

Figure 3. When a multivariate image 5 and external knowledge y for some regions in the image are available, a regression model can be constructed. Because of the collinearities expected in the variable, a regression in latcnt variables is preferable. This could be principal component regression (PCR) or partial least squares regression (PLS). The regression model allows prediction of the external knowledge lor pixels where it was not available. This gives the predicted image Y. One also obtains latent variable images (here as T, , T1 and T,) and distance-to-model images

(from the residual E)

with, for example, principal component regression (PCR) or partial least squares regression

The latent variables constructed for the regression model form images that can be inspected visually. Also the residual of the multivariate image (the part of it not used to build the regression model) is in image form. It can also be used to construct statistical estimators of model fit. Finally, when the external information is only for part of the multivariate image, the regression model allows a prediction. This gives a complete image where every pixel is the predicted value of the external data. A graphical overview of this is given in Figure 3.

When the external data are in the form of chemical concentrations, the predicted image in the above paragraph is a concentration image. When such is possible, it constitutes a very advanced form of chemical image analysis.

(PLS)


IMAGE ANALYSIS ON NON-IMAGE DATA

Both univariate and multivarite image analysis are useful for extracting information from image data. The methods are constructed for handling large arrays of data. In chemistry there are also non-imaging techniques that generate large 2D and 3D arrays of data. These are the hyphenated methods of chemical analysis. The result of a 2D hyphenated measurement can be considered as an image as soon as its size goes over 64x64 points. When the data are collected for lots of samples, a three-way array of data can be constructed, with the third way being samples. This three-way array has properties similar to that of a multivarite image and can be treated in the same way. A similar reasoning can be used for three-way hyphenated measurements leading to four-way arrays when many samples are measured. The sizes of the arrays, speed of calculation considerations and representation of results make image analysis techniques promising for these arrays resulting from non-imaging techniques. The advantages for multivariate calibration and exploratory data analysis are easily understood here.

Some hyphenated techniques where this could be made useful are LC-UV (liquid chromatography-ultraviolet spectrometry), GC-MS (gas chromatography-mass spec- rometry), GC-IR (gas chromatography-infrared spectrometry), excitation-emission fluorescence spectrometry, 2D NMR, 3D NMR and MS-MS (mass spectrometry-mass s p e c t r ~ m e t r y ) . " ~ ~ ~ See also Figure 4.

Figure 4. Large data arrays such as those obtained from chromatography-spectrometry combinations may also be treated as images. When measurements are made for a series of samples, a stack of such 'images' builds up a three-way

data array similar to a multivariate image

CONCLUSIONS

Many types of physical parameters (variables) can be used for imaging purposes. Some variables enable the extraction of chemical information. The use of many variables for the same scene or object gives rise to multivariate images. Multivariate image analysis uses

P. GELADI AND K . ESBENSEN 428

principles similar to those of multivariate data analysis. The chemical information extracted from a univariate or multivariate image can be of two levels: histochemical or concentration. Classification methods can be used for histochemical data. The determination of concentration requires the use of univariate of multivariate regression methods.

An advantage of image analysis methods is that interpretation of results can be based on visual observation instead of looking at lists of numbers. This a very important asset for multivariate analysis.

A conclusion is that with careful collection and proper preprocessing, images can give rise to chemical information. For univariate images chemical information can only be extracted in simple cases. More complex situations require multivariate images where the selection of the variables used becomes of major importance. The field of multivarite image analysis is one where both statistical methods and technology are expected to evolve to give an improvement over the present situation.

ACKNOWLEDGEMENTS

We would like to acknowledge Christer Albano and Svante Wold, Umeb University, Umei, Sweden for support and interesting discussions. The Peat Dewatering project of Umei, Sweden provided funding. Part of the contents of this paper was presented at a double lecture held in Trieste, Italy on 21 June 1988. Paolo Linda, University of Trieste, Italy and Sergio Clementi, University of Perugia, Italy are thanked for helping to organize these lectures.

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Can image analysis provide information useful in chemistry?

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