Author: Xu, Zi-xin
Title: Applications of halftoning techniques in 3d profilometry and reversible color-to-grayscale conversion
Advisors: Chan, Yue-hee (EIE)
Degree: Ph.D.
Year: 2017
Subject: Hong Kong Polytechnic University -- Dissertations
Image processing -- Digital techniques
Computer graphics
Department: Department of Electronic and Information Engineering
Pages: xxv, 168 pages : color illustrations
Language: English
Abstract: Digital halftoning is a technique originally proposed to render a gray scale image with binary value pixels. It is able to shift the quantization noise to the high frequency band. Accordingly, the quantization noise can be removed through the lowpass filtering effect of human visual systems to make a binary image visually identical to the original gray level image. Digital halftoning was successfully extended to render color images and it has been widely used in printing applications nowadays. However, its application in other areas is still limited. The objective of this work is to explore possible applications of digital halftoning in areas other than printing. This thesis reports some findings that we had and some contributions that we made during our study. In particular, the focus will be on the application of digital halftoning in (1) 3D profilometry and (2) reversible color to grayscale conversion. Digital fringe projection technique has been widely used in commercial 3D depth map acquisition in the past decades due to its simplicity, reliability and flexibility. When it is used, fringe patterns are projected onto the object for evaluating its depth information. Phase-shifting sinusoidal patterns are popular patterns used in digital fringe projection. To support real-time measurement and get rid of the luminance nonlinearity of a projector, the binary defocusing method has been proposed to replace sinusoidal patterns with binary patterns. In its practical realization, the binary patterns should be good approximations of the sinusoidal patterns and contain only high frequency approximation errors. Since the projector is defocused, the patterns projected onto the object are blurred and the high frequency approximation error can be removed to some extent. Obviously, halftoning can be applied to produce binary fringe patterns based on the target sinusoidal fringe patterns. From signal processing point of view, the binary fringe patterns usedin binary defocusing method can be considered as 1-bit quantization outputs of sinusoidal fringe patterns. Obviously, the projected fringe patterns impact the measurement quality directly and hence it is a good move to improve the quality of a quantized fringe pattern by increasing its quantization levels. By making use of the fact that a digital-light-processing projector can actually project color patterns via three different channels simultaneously, we proposed a method to project octa-level fringe patterns at no extra cost as compared with projecting binary fringe patterns. Accordingly, while the measurement performance can be improved, the advantages of binary defocusing can be maintained. In other words, it still supports real-time measurement and does not need to handle the luminance nonlinearity of a projector. A framework for optimizing octa-level fringe patterns to support this projection method was also proposed in this work. The extent of defocusing plays a critical role in determining the quality of the defocused fringe patterns. In real situations, it is impossible to control it precisely and hence the fringe patterns should make their performance robust to it. To respond to this issue, conventional fringe pattern generation schemes optimize halftone patterns under different conditions (e.g. different patch sizes and different defocusing extent) and then, from the optimized results, pick the one which is the most robust to defocusing conditions. This pick-the-best-from-the-available approach is passive to some extent and makes the optimization effort grow in multiples. To provide flexibility and reduce effort, the optimization processes of recent binary fringe pattern generation schemes are generally patch-based by making use of the property that a sinusoidal fringe pattern is periodic. In general, they optimize one single halftone patch to make its defocused output close to a patch of a sinusoidal fringe pattern and then tile it repeatedly to construct all full-size fringe pattern.We have three observations on this common strategy as follows: (1) The distortion of the tiling result with respect to an ideal sinusoidal fringe pattern is periodic and contains strong harmonics, which affects the measuring performance remarkably. (2) The fringe period is bound to be an integer multiple of 3. (3) It introduces extra constraint for the optimization process.
To solve all these problems, we proposed a framework for generating aperiodic octa-level fringe patterns based on optimized patches. The produced fringe patterns can significantly lower the noise floor and suppress the harmonic distortion in the constructed depth map. Accordingly, the achieved depth measuring performance can be significantly improved. Special care is also taken during the optimization of the patches in our framework such that the depth measuring performance is robust to the variation of fringe period and defocusing extent. Though conventional fringe pattern generation schemes formulate the pattern generation as an optimization problem, the problem is generally solved by iteratively refining an initial estimate due to its unaffordable complexity. This strategy cannot guarantee a global optimum in terms of an objective function. When the refining step is not flexible, the solution can be biased to the initial estimate and its performance can be far from the optimal. Besides, a poor initial estimate can easily guide the optimization process to reach a poor local optimum at the end. In view of this, a better initial estimate and a flexible refining scheme would definitely be helpful to get better fringe patterns. By fulfilling these two demands and extending the idea of our previous work, we further developed a novel method to generate patch-based octa-level fringe patterns for improving the measuring performance of a 3D surface measuring system. Specifically, the optimized patches can be flexibly and seamlessly tiled to form octa-level fringe patterns. As compared with the fringe patterns generated with our previously proposed method, their produced depth maps contain no harmonic distortion along any direction instead of just one single direction. Reversible color-to-grayscale conversion (RCGC) aims at embedding the chromatic information of a full color image into its grayscale version such that the original color image can be reconstructed in the future when necessary. Conventional RCGC algorithms tend to put their emphasis on the quality of the reconstructed color image, which makes the color-embedded grayscale image visually undesirable and suspicious. As an output of this study, a novel RCGC framework that emphasizes the quality of both the color-embedded grayscale image and the reconstructed color image simultaneously is proposed. Its superiority against other RCGC algorithms is mainly achieved by developing a color palette that fits into the application and exploiting error diffusion to shape the quantization noise to high frequency band. The improved visual quality of the color-embedded grayscale image makes the image appears as a normal image. It does not catch the attention of unauthorized people and hence the embedded chromatic information can be protected more securely. The color palette used in the proposed RCGC framework is critical to the conversion performance. To fit into the application, we proposed a palette generation algorithm to generate an image-dependent palette that bears two properties. First, palette colors are sorted and indexed according to their luminance values such that the index plane looks closely to the luminance plane of the original color image. Second, consecutive colors in the palette form a three-dimensional enclosure in the color space to cover as many pixel colors that have the same luminance values as the involved palette colors as possible. Theoretically, with the halftoning technique, any specific color inside the enclosure can be rendered with the palette colors that form the enclosure. The aforementioned palette generation algorithm was further improved in an extended study. The idea comes from two observations. First, halftoning does not work properly when the region having the color to be rendered is very small in the image and the color is very different from the available palette colors. Second, from mean square error point of view, using a palette color directly to replace a pixel color can be more efficient than rendering it with halftoning. While our first proposed palette generation algorithm concerns whether a color can be rendered with halftoning in ideal situations, the improved palette generation algorithm considers whether a color can be effectively rendered in practical situations. We proposed a measure to estimate the effectiveness and appropriateness of using halftoning to render a specific color in a spatial region. The measure is incorporated into the objective function to optimize the color palette. As a result, the color palette can work with our proposed RCGC framework in a better way and achieve a better RCGC performance. In this thesis, we present some ideas for the applications of digital halftoning in 3D profilometry and reversible color to grayscale conversion. As a tool of noise shaping, digital halftoning can be applied in different areas. We expect there will be more novel application ideas coming in future.
Rights: All rights reserved
Access: open access

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