Image segmentation and pigment mapping of cultural heritage based on spectral imaging

The goal of the work reported in this dissertation is to develop methods for image segmentation and pigment mapping of paintings based on spectral imaging. To reach this goal it is necessary to achieve sufficient spectral and colorimetric accuracies of both the spectral imaging system and pigment mapping. The output is a series of spatial distributions of pigments (or pigment maps) composing a painting. With these pigment maps, the change of the color appearance of the painting can be simulated when the optical properties of one or more pigments are altered. These pigment maps will also be beneficial for enriching the historical knowledge of the painting and aiding conservators in determining the best course for retouching damaged areas of the painting when metamerism is a factor. First, a new spectral reconstruction algorithm was developed based on Wyszecki’s hypothesis and the matrix R theory developed by Cohen and Kappauf. The method achieved both high spectral and colorimetric accuracies for a certain combination of illuminant and observer. The method was successfully tested with a practical spectral imaging system that included a traditional color-filter-array camera coupled with two optimized filters, developed in the Munsell Color Science Laboratory. The spectral imaging system was used to image test paintings, and the method was used to retrieve spectral reflectance factors for these paintings. Next, pigment mapping methods were brought forth, and these methods were based on Kubelka-Munk (K-M) turbid media theory that can predict spectral reflectance factor for a specimen from the optical properties of the specimen’s constituent pigments. The K-M theory has achieved practical success for opaque materials by reduction in mathematical complexity and elimination of controlling thickness. The use of the general K-M theory for the translucent samples was extensively studied, including determination of optical properties of pigments as functions of film thickness, and prediction of spectral reflectance factor of a specimen by selecting the right pigment combination. After that, an investigation was carried out to evaluate the impact of opacity and layer configuration of a specimen on pigment mapping. The conclusions were drawn from the comparisons of prediction accuracies of pigment mapping between opaque and translucent assumption, and between single and bi-layer assumptions. Finally, spectral imaging and pigment mapping were applied to three paintings. Large images were first partitioned into several small images, and each small image was segmented into different clusters based on either an unsupervised or supervised classification method. For each cluster, pigment mapping was done pixel-wise with a limited number of pigments, or with a limited number of pixels and then extended to other pixels based on a similarity calculation. For the masterpiece The Starry Night, these pigment maps can provide historical knowledge about the painting, aid conservators for inpainting damaged areas, and digitally rejuvenate the original color appearance of the painting (e.g. when the lead white was not noticeably darkened)

Correspondence Between Continuous and Discrete 2 Flux Models for Reflectance and Transmittance of Diffusing Layers

This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka's layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (discrete two-flux model). The compatibility of these two models is shown. In particular, the Kubelka–Munk reflectance and transmittance expressions are retrieved, using Kubelka's layering model, with mathematical arguments using infinitely thin sublayers. A new approach to the Kubelka–Munk expressions is thus obtained, giving, moreover, new details for physical interpretation of the Kubelka–Munk theory

Modeling and Halftoning for Multichannel Printers: A Spectral Approach

Printing has been has been the major communication medium for many centuries. In the last twenty years, multichannel printing has brought new opportunities and challenges. Beside of extended colour gamut of the multichannel printer, the opportunity was presented to use a multichannel printer for ‘spectral printing’. The aim of spectral printing is typically the same as for colour printing; that is, to match input signal with printing specific ink combinations. In order to control printers so that the combination or mixture of inks results in specific colour or spectra requires a spectral reflectance printer model that estimates reflectance spectra from nominal dot coverage. The printer models have one of the key roles in accurate communication of colour to the printed media. Accordingly, this has been one of the most active research areas in printing. The research direction was toward improvement of the model accuracy, model simplicity and toward minimal resources used by the model in terms of computational power and usage of material. The contribution of the work included in the thesis is also directed toward improvement of the printer models but for the multichannel printing. The thesis is focused primarily on improving existing spectral printer models and developing a new model. In addition, the aim was to develop and implement a multichannel halftoning method which should provide with high image quality. Therefore, the research goals of the thesis were: maximal accuracy of printer models, optimal resource usage and maximal image quality of halftoning and whole spectral reproduction system. Maximal colour accuracy of a model but with the least resources used is achieved by optimizing printer model calibration process. First, estimation of the physical and optical dot gain is performed with newly proposed method and model. Second, a custom training target is estimated using the proposed new method. These two proposed methods and one proposed model were at the same time the means of optimal resource usage, both in computational time and material. The third goal was satisfied with newly proposed halftoning method for multichannel printing. This method also satisfies the goal of optimal computational time but with maintaining high image quality. When applied in spectral reproduction workflow, this halftoning reduces noise induced in an inversion of the printer model. Finally, a case study was conducted on the practical use of multichannel printers and spectral reproduction workflow. In addition to a gamut comparison in colour space, it is shown that otherwise limited reach of spectral printing could potentially be used to simulate spectra and colour of textile fabrics

A Unified model for color prediction of halftoned prints

This study introduces a new model and a new mathematical formulation describing the light scattering and ink spreading phenomena in printing. The new model generalizes the classical Kubelka-Munk theory, and unifies it with the Neugebauer model within a single mathematical framework based on matrices. Results like the Saunderson correction, the Clapper-Yule equation, the Murray-Davis relation and the Williams-Clapper equation are shown to be particular cases of the new model. Using this new theoretical tool, the reflection spectra of 100 samples printed on high quality paper by two different ink-jet printers were computed with an average prediction error of about ΔE = 2.1 in CIELAB

A model for colour prediction of halftoned samples incorporating light scattering and ink spreading

A model for color prediction of halftoned samples incorporating light scattering and ink spreading was presented. The spreading process was modeled by enlarging the drop impact according to the configuration of its neighbors and the state of the surface. The spectra of halftoned samples produced with one ink were predicted with an average prediction error or about δE=1.4 in CIELAB. For two halftoned ink layers, good spectral predictions were achieved with an average error of about δE=2.1 in CIELAB

Digital Color Imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided

Virtual electro-photographic printer model

A halftone image in the computer is a bitmap matrix that contains either 0 or 1 , where 0 means the printer will not deposit any toner onto a paper and 1 means the printer will deposit some amount of toner onto a paper. The amount of toner that is put by the printer onto a paper for a given input signal pattern is characterized. The hypothesis was that the distribution of toner mass on the paper for a given input matrix pattern can be modeled with a toner point spread function, a toner transfer efficiency function, and a noise function. In order to study toner mass distribution printed on paper, it is necessary to develop an analytical technique for measuring the distribution of toner mass. The analytical technique used in this thesis is an optical analysis based on light transmitted through the printed sample. This analytical technique was calibrated against a gravimetric analysis. Linear relation between the optical analysis and gravimetric analysis indicates that the technique can be used for measuring spatial distribution of printed toner mass on a micro-scale. Guided by experimental measurements of toner mass distribution, a quantitative model of the three printer functions, the spread function, the toner delivery function, and the noise function, were characterized. These functions were used to construct a printer function that was used to compare the efficiency of different halftone patterns. The result of the printer model was extended to include the optical point spread function of the paper. This provided a complete printing model that simulated both physical and optical dot gain