6th World Conference on NDT and Microanalysis in Diagnostics and Conservation of Cultural and Environmental Heritage, Rome, 1999 May. Published by AIPnD, email: aipnd@numerica.it

TABLE OF CONTENTS

Abstract Introduction Methods and algorithms Added Information Computer Graphics Techniques Extracted Information Computer Graphics The Richardson-Lucy algorithm Simulated annealing methods Conclusions

Abstract

Computed Aided treatment of images can be usefully exploited in the field of Historical and Cultural Heritage conservation, where often there is a need for analysis of noisy, old or damaged pieces of artwork or images. In this paper we discuss and compare different algorithms that can be useful for retrieval of information from images, in terms of their efficiency and precision. In particular, the problem of refocusing of blurred images of 3D objects is discussed, using blind deconvolution and simulated annealing technique.

Introduction

In these last years, digital treatment of images has been widely used in many different fields, including astrophysical, medical, geophysical and military research. In this paper, we will focus our attention to the application of Computer Graphics methods and algorithms in Cultural Heritage conservation. In the following, we will divide our discussion in two logically separated parts: at first, we will present methods and computer aided techniques which may help both in enhancing the comprehension of a given piece of artwork or may be useful in analysing the artwork in view of its restoration. We will call this procedure Added Information Computer Graphics, in order to make clear that the computer is used in this case as a mere instrument for putting, although virtually, an external information into the digitally acquired image. This kind of procedure in general relies on the use of commercial software for image treatment as a tool for the conservator whose experience, at the end, is the source of the information added to the artwork (image). The second section of this paper will deal with the Extracted Information Computer Graphics methods; in this case, the hidden information is not externally added to the image, but extracted with the use of given algorithms. A typical example of EICG is the restoration of old blurred photographs or reconstruction of aerial photographs of archaeological sites. EICG methods are in general iterative, non-linear and time-consuming. Restoration of a single image could take several thousand iterations and many hours of processing to achieve. However, a proper choice of the computer algorithm and the use of acceleration techniques can reduce the expense of computing resources and time.

Methods and algorithms

Added Information Computer Graphics Techniques
In these last years, we have witnessed a dramatic increase in performance and reduction in costs of desktop personal computer, which associates to a wide diffusion of computers in academic research and professional activities. At the same times, highly sophisticated software has become available which allows professional treatment of images at practically no cost. Given this situation, it seems natural to discuss the use of such systems in the field of Cultural Heritage conservation; in reality, one should essentially wonder why AICG techniques are still relatively rare in this field, instead of presenting the clear advantages associated with them.

Fig 1: Virtual restoration of a painting (at right) compared with the original image (at left)

Fig 2: Virtual restoration of a painting (at right) compared with the original image (at left)

In any case, we will here consider two possible applications of AICG methods in Cultural Heritage: AICG as an aid before actual restoration of the artwork, and AICG as a tool for enhancing the comprehension of the damaged piece of artwork (Virtual Restoration). In the first typology of intervention, a computer software for image treatment is used for elaborating digital copies of the artwork with the aim of identifying the damaged parts of the object and proposing the possible intervention (for example, choosing the proper colours in order to fill the gaps in the surface). It's worth mentioning that a great deal of work has been performed in this field by *** et al. [**] in the framework of CNR Project "Cultural Heritage".

In some cases, an actual intervention of restoration on the artwork might be impossible, or inappropriate. However, AICG techniques may be usefully exploited even in this case for virtually reconstructing the object in a state similar to the original, thus helping in appreciating the intrinsic artistic value of the artwork, which is often hidden under its historical value.

What are the limits of AICG in Cultural Heritage studies and conservation? As usual, the experience and sensibility of the conservator is essential for maintaining the Virtual Restoration process in the strictly scientific field; however, although excesses are possible, one should not forget that all these methods are essentially reversible and clearly will not damage in any way the original artwork.

Extracted Information Computer Graphics
In many cases, some information might be hidden in the image to be treated that may be revealed with the use of proper computer techniques and algorithms. As opposite to AICG, Extracted Information Computer Graphics often relies on the use of specialised non-commercial software and is in general rather consuming in terms of time and computer resources. On the other hand, EICG techniques rely less heavily on the experience of the operator, so that they can be often be run automatically. A typical field of application of EICG is the treatment of blurred images, which is a problem often present when dealing with old historical pictures or aerial photographs of archaeological sites. In many cases, the picture is unique, or it might be very difficult or expensive to take a new shot, thus justifying the time and computer resources spent in its digital elaboration.

Let us discuss the main features of EICG using the example of a picture out of focus. The blurred picture B may be interpreted as the convolution of a given point spread function (PSF) with the 'perfect' picture P

B = PSF Ä P

(in the case of a out of focus picture the PSF may be considered as a gaussian function whose width is related to the degree of blurring of the image). Graphically, we can write the above equation as:

The purpose of EICG in this case is the 'extraction' of the information (P) from B; a naive approach to the problem would be the use of Fourier transforms, assuming the functional dependence of PSF is know:

Unfortunately, this simple equation is not applicable in real image treatment, because of the noise amplification effect, which is intrinsic with this approach. A modification of eq.(1) that is less prone to noise amplification effect is based on the use of a low-pass filter for reducing the noise:

This method is often used in commercial image treatment software as a de-blurring algorithm but, despite its velocity, it still gives unacceptable results in most cases when applied in the field of Cultural Heritage.

Better results are obtained by the use of iterative methods. We will discuss here two of them: the Richardson-Lucy algorithm and the so-called Simulated Annealing method. The approaches of the two methods are completely different; in the first case the PSF of the system is assumed known and independent on the image co-ordinates, while the second approach does not require the knowledge of the PSF, which is determined iteratively at the same time of the reconstructed image. On the other hand, simulated annealing techniques are more time and computer resources consuming than R-L algorithm.

The Richardson-Lucy algorithm
The Richardson-Lucy algorithm was developed in order to converge towards the maximum likelihood solution for data obeying to Poisson statistics, which is the typical case of noise in digital images. The joint likelihood of getting the observed intensity in each pixel of the image given the expected intensity I is

The maximum likelihood solution occurs where all partial derivatives of L with respect to P are zero

which gives the RL iteration as

Fig 3: Refocusing of the image of a Bizantine icon (at right) compared with the original image (at left)

The RL algorithm, although more robust against noise amplification, is characterised by the occurrence of 'speckles' which give a grainy appearance to the reconstructed images. Recently, a modification of RL algorithm was proposed by White [**], which 'damps' the noise amplification process using an adaptive stopping criterion to modify the likelihood function so that it becomes flatter in the vicinity of a good solution. This Damped Richardson-Lucy algorithm gives rather smooth results. Examples of its application are given in fig.(3)

Simulated annealing methods
The process of reconstruction of the original image from the blurred one without prior knowledge of the PSF is called 'blind deconvolution'. According to this approach, both the image P and the PSF are deducted by the blurred image B using a MonteCarlo method which iteratively minimises the difference between the actual blurred image and the 'theoretical' re-blurred image given by the convolution of reconstructed P and PSF at step i of the iteration. It must be noted that the couple of functions corresponding to the blurred image itself and a delta-like PSF (i.e., no blurring at all) give an absolute minimum of the above defined function. In other words, the best reconstruction is the original image, which obviously does not give any useful information. In order to obtain valid results, blind deconvolution methods should either put some constraint on the PSF or the information about sharpness of the image must be inserted into the function to be minimised, i.e. we must require a minimum of the difference between original and theoretically re-blurred image subject to the condition that the resulting image is more sharp than the original one. This condition is called a prior term which represents a constraint to be optimised together with the minimisation of the difference between original and re-blurred image. The simpler method for reconstructing the image P is the steepest descent methods, a well established algorithm which moves towards the minimum of the function along the steepest direction. A drawback of this method is the fact that the solution may be trapped in local minima instead of reaching the absolute minimum (the best reconstructed image); if the blurred image is not very far from the reconstructed one, this is a reasonable and fast approach. However, in general case other algorithms, although more lengthy and complex, assure a better convergence to the optimum solution. In case of the so called 'simulated annealing' method the steepest descent algorithm may be used, but occasionally a 'worst' solution may be accepted (with a given probability). This is done in order to give the possibility to the solution of escaping from local minima and hopefully reaching the absolute minimum corresponding to the optimum reconstructed image. The process is thus assimilated to a physical system subjected to the effect of a temperature T, which slowly reduces while the algorithm converges

Conclusions

In this paper we have presented a discussion of the main applications of Computer Aided Image Processing in the field of Cultural Heritage, along with examples of their application. In conclusion, we hope to have demonstrated that Computer Graphics can be extremely helpful both as a preliminary aid before actual restoring of pieces of artwork, as a method for enhancing the comprehension of the artistic object or as a technique for getting 'hidden' information from the image. All the techniques illustrated require standard and cheap computer systems, not more powerful than the ones used by everyone for word processing or administration. We believe that in the near future Computer Aided methods will assume a growing importance in the field of Cultural Heritage, and we hope that our country would benefit of them, as it deserves.