Sampling and interpolation of static images : a perceptual view Citation for published version (APA): Nijenhuis, M. R. M. (1993). Sampling and interpolation of static images : a perceptual view. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR404755 DOI: 10.6100/IR404755 Document status and date: Published: 01/01/1993 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. 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J .H. van Lint, voor een commissie aangewezen door het College van Dekanen in het openbaar te verdedigen op vrijdag 29 oktober 1993 om 16.00 uur door Marco Reinirus Maria Nijenhuis geboren te Rheden Dit proefschrift is goedgekeurd door de promotoren: prof. dr. ir. J.A.J. Roufs prof. dr. H. Bouma en de copromotor dr. ir. F.J.J. Blommaert Druk: Wibro dissertatie drukkerij, Belmond © M.R.M. Nijenhuis, 1993 CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG Nijenhuis, Marco Reinirus Maria Sampling and interpolation of static images : a perceptual view / Marco Reinirus Maria Nijenhuis. - Eindhoven : Technische Universiteit Eindhoven Proefschrift Eindhoven. - Met lit. opg. - Met samenvatting in het Nederlands. ISBN 90-386-0412-2 Trefw.: beeldweergave ; kwaliteit. aan Ria, Pap, Mam en Rene Contents 1 Introduction 7 2 A perceptual error measure for sampled and interpolated im- ages - Theory 11 2.1 Abstract . 11 2.2 Introduction . 11 2.3 The perceptual error measure 12 2.3.1 Perceptual impairment and perceptual image quality . 13 2.3.2 Combination rule for perceptual impairments . 16 2.3.3 Perceptual strength and impairment of an artefact 16 2.3.4 Physical parameters and perceptual strengths . 17 2.4 Interpretation of the perceptual error measure . 23 2.5 Discussion ................ 25 Appendix 2.A Periodic structure experiment 26 3 Perceptual error measure for a single-edged image 31 3.1 Abstract . 31 3.2 Introduction . 31 3.3 Rationale of single-edged images 32 3.4 Perceptual error measure 34 3.5 Experiments . 36 3.6 Minkowski exponent experiment 36 Contents 5 3.6.1 Method 37 3.6.2 Flesults 38 3. 7 Contrast and luminance experiment 42 3.7.1 Method . 42 3.7.2 Perceptual strength of blur 45 3. 7.3 Perceptual strength of periodic structure . 46 3.7.4 Perceptual strength of complement of brightness and complement of brightness contrast 49 3.7.5 Flegularization parameter for blur . 50 3.7.6 Performance of the perceptual error measure 53 3.8 Discussion . 56 Appendix 3.A The value and the standard deviation of the a0 and mo parameters . 62 Appendix 3.B Standard deviation of the regularization parameter for blur . 63 4 Perceptual error measure for complex black and white images 65 4.1 Abstract ... 65 4.2 Introduction . 65 4.3 Perceptual error measure 66 4.4 Complex black and white experiment . 67 4.4.1 Method . 67 4.4.2 Perceptual strength of blur and periodic structure 72 4.4.3 Flegularization parameter for blur . 75 4.4.4 Performance of the perceptual error measure 76 4.5 Discussion . 78 5 Perceptual error measure for complex colour images 85 5.1 Abstract ... 85 5.2 Introduction . 85 5.3 Modulation depth as a function of colour 86 6 Contents 5.4 Perceptual error measure . 88 5.5 Complex colour experiment 90 5.5.1 Method . 90 5.5.2 Perceptual strength of blur and periodic structure 94 5.5.3 Regularization parameter for blur . 96 5.5.4 Performance of the perceptual error measure 98 5.6 Discussion . 98 6 Epilogue 109 6.1 Perceptually optimal sampling 109 6.2 Two-dimensional sampling structures . 113 6.3 Technical aspects of sampling and interpolation functions 115 6.4 General conclusions . 116 References 117 Summary 121 Samenvatting 122 Acknowledgement 124 Curriculum Vitae 125 Chapter 1 Introduction The majority of electro-optical displays including liquid-crystal displays (LCD) and cathode ray tubes (CRT) use sampling and interpolation techniques. Sam­ pling means that the images are no longer continuous but discrete. The samples are taken at regular intervals in both space and time. Within limits, the samples can have arbitrary values, i.e. they are not quantized. Sampling is applied in at least one of the two spatial dimensions. There are several degrees of freedom in the design of the sampling structure such as the sampling density and the sampling geometry. Interpolation fills in the gaps between the samples. The type and the degree of interpolation are free parameters. In practice, however, the interpolation functions are positive-valued and extend over a non-zero in­ terval in both space and time. This interval is usually smaller than the distance between the samples. The spatial extension of the interpolation function can be arbitrarily expanded by combining the display with an optical filter placed in front of the display. Owing to sampling and interpolation the images reproduced by the display differ from the original images. The choice of the display and filter parameters influences the visibility of sampling and interpolation artefacts such as flicker, periodic structure and blur. Pre-filters, which process the electrical image signal before it is displayed, may reduce the strength of such artefacts and may, at the same time, introduce other artefacts. These filters can, for instance, deblur the displayed images. Again, the type and degree of filtering are free parameters. Measurements of perceptual image quality, i.e. the degree of excellence of an image (Roufs & Bouma, 1980), should be used to evaluate sampled and interpolated images produced by a display. It is possible to distinguish be­ tween appreciation-oriented and performance-oriented perceptual image qual­ ity (Roufs, 1992). The former is a measure ofimage fidelity as opposed to the latter, which denotes the human ability to extract relevant information (Pratt, 1978). In this thesis we are concerned with appreciation-oriented perceptual image quality of sampled and interpolated images. In general, the perceptual image quality is not related linearly to the physical parameters specifying the 8 Chapter 1 Introduction sampling and interpolation process. A comparison of displays with different sampling and interpolation combinations should be made by considering the differences of the perceptual image quality values of images produced by these displays. Perceptual image quality enables the perceptual optimization of the physi­ cal display parameters specifying the sampling and interpolation process. More specifically, it enables the specification of the values of the display parameters for which the perceptual image quality of the displayed images is maximal. For example, Nijenhuis & Blommaert (1990) use perceptual image quality to determine perceptually optimal parameters of an optical interpolation filter for sampled images. Alternatively, we can determine all parameter settings that satisfy some perceptual image quality criterion. From these settings we can then choose the one that is economically most feasible. Much effort has been spent over the last decades to formulate quantitative perceptual error measures for the perceptual quality of sampled and interpo­ lated images. These perceptual error measures predict the loss of perceptual image quality from the physical parameters specifying the sampling and in­ terpolation process. Although perceptual image quality can also be assessed by means of subjective evaluation techniques such as category scaling, this is an elaborate and time-consuming process. Obviously, the predicted values of perceptual image quality should be consistent with the results of subjective evaluations. At present there are numerous quantitative error measures for sampled and interpolated images. This is probably due to the fact that sampling and interpolation can be described mathematically very well. Undoubtedly the most important theorem in this field is the sampling theorem introduced by Shannon (1949), Whittaker and Kotel'nikow. The theorem states that a contin­ uous band-limited signal can be reconstructed without loss of information from a discrete series of regularly spaced samples.