Image Segmentation and Pigment Mapping in Spectral Imaging
Spectral imaging techniques have been well developed in the last ten years for art conservation science. Spectral reconstruction algorithms have achieved sufficiently high accuracy to predict specific pigments and their concentrations of each pixel on works of art. Digital rejuvenation can be promptly performed on works of art based on the pigment mapping to correct changed color or repaint discolored parts. In our pilot experiment, the painting was made of ten Gamblin artist oil paints plus white paint. A spectral image of the painting was derived from multi channel camera signals. To overcome the difficulty of unmixing a large spectral image, the image was first segmented using k Means classification in CIELAB color space. Within each segmented region, based on its colorimetric property, a subgroup of pigments was selected from a predefined pigment database. Pigment mapping was then implemented for each pixel in this segmented region with this subgroup of pigments based on two constant Kubelka Munk theory. By focusing on a subgroup of pigments rather than unmixing with the entire pigment database for each pixel, the computation efficiency was greatly improved. Introduction The characterization of materials constituting paintings is essential for the historical knowledge of the painting and for retouching (i.e. inpainting) the lost or damaged areas in the painting. Modern analytical techniques provide comprehensive information on the chemical composition of the materials by means of minute quantities taken from the objects. [1] However, there is a clear desire to use non destructive methods. There are two main visible spectrum noninvasive approaches: spot spectroscopy and imaging spectroscopy. Though spot spectroscopy is expected to have higher accuracy than imaging spectroscopy, it is only possible to measure the color at a limited number of points on the surface of the painting over a fixed aperture. This means that the measurement sites have to be selected and marked carefully. On the other hand, imaging spectroscopy avoids the difficulty by simply measuring the whole surface. With enormous development of imaging spectroscopy in the last ten years, the spectral accuracy of this technique has been improved to a great extent so that spectral images have been used for documentation, analytical assessment and digital rejuvenation. [2] Additionally, it is possible to identify the pigments and quantify their constituents for each pixel of the spectral image. [3] This paper presents further investigation into the potential of spectral imaging techniques for pigment mapping. Pigment mapping is of great importance for conservators to inpaint the lost or damaged areas of paintings. It is generally difficult to avoid metamerism if those areas are restored by visual color matching to the surrounding undamaged surface. Berns [4] suggested that the inpainted areas should ideally have identical optical (spectral, color and transparency) and geometric (gloss, texture and impasto) properties. In this pilot experiment, spectral matching, rather than conventional color matching, was achieved by pigment mapping. Reference [6] investigates the potential of multispectral imaging for pigment identification in paintings. It assumes that there are only pure pigments or mixtures of these pigments with either a white or black colorant. It also assumes that these mixtures transform the reflectance spectrum of a pigment in an approximate linear fashion. However, it is known that the logarithm of the absorption K and scattering S ratio is the most invariant to changes in concentration. [4] Thus, pigment mapping should not be done in reflectance space, but in K S space. The Kubelka Munk (K M) theory has been widely used in the paint industry for over 50 years. [7,8] It is an optical model that establishes the relationship between surface reflectance and colorant formulation, layer thickness and substrate reflectance. References [4] and [5] applied single constant K M theory to select multiple pigments for inpainting using spot spectroscopy. Reference [9] used a computer match prediction model based on K M theory to select pigment recipes that give non metameric matches, but only give prime attention to blue pigments. In this experiment, the test target was a small oil painting made of ten chromatic pigments and titanium white. It was assumed that every pixel was made of at most four pigments. Thus, it makes more sense to map each pixel using a subgroup rather than all of the pigments. The image was first segmented using k Means [10] classification into five different clusters in CIELAB (a*b* color space. Then, up to four pigments were selected to map every pixel in each cluster based on colorimetric information. This approach successfully and efficiently identified and spatially mapped pigments for each pixel in the image. Theory The general model of K M theory can be simplified for an opaque surface. [8] The simplified version describes the relationship between the optical (spectral reflectance) and material properties (the ratio between absorption and scattering coefficients) as follows: K S