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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
PIXELS & PAINTINGS "The discussion is firmly grounded in established art historical practices, such as close visual analysis and an understanding of artists' working methods, and real-world examples demonstrate how computer-assisted techniques can complement traditional approaches." --Dr. Emilie Gordenker, Director of the Van Gogh Museum The pioneering presentation of computer-based image analysis of fine art, forging a dialog between art scholars and the computer vision community In recent years, sophisticated computer vision, graphics, and artificial intelligence algorithms have proven to be increasingly powerful tools in the study of fine art. These methods--some adapted from forensic digital photography and others developed specifically for art--empower a growing number of computer-savvy art scholars, conservators, and historians to answer longstanding questions as well as provide new approaches to the interpretation of art. Pixels & Paintings provides the first and authoritative overview of the broad range of these methods, which extend from image processing of palette, marks, brush strokes, and shapes up through analysis of objects, poses, style, composition, to the computation of simple interpretations of artworks. This book stresses that computer methods for art analysis must always incorporate the cultural contexts appropriate to the art studies at hand--a blend of humanistic and scientific expertise. * Describes powerful computer image analysis methods and their application to problems in the history and interpretation of fine art * Discusses some of the art historical lessons and revelations provided by the use of these methods * Clarifies the assumptions and applicability of methods and the role of cultural contexts in their use * Shows how computation can be used to analyze tens of thousands of artworks to reveal trends and anomalies that could not be found by traditional non-computer methods Pixels & Paintings is essential reading for computer image analysts and graphics specialists, conservators, historians, students, psychologists and the general public interested in the study and appreciation of art.
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Contents
Cover
Table of Contents
Title Page
Copyright
About the Cover
Dedication
List of Figures
List of Tables
List of Algorithms
Preface
Giovanni Morelli and the birth of “scientific” connoisseurship
Overview
Intended audience
Prerequisites
Acknowledgements
1 Digital imaging
1.1 Introduction
1.2 Electromagnetic radiation and light
1.3 Interaction of electromagnetic radiation with art materials
1.4 Cameras and scanners
1.5 Parameters for image acquisition in the visible
1.6 Reading digital images of art on–screen
1.7 Infrared photography and reflectography
1.8 Ultraviolet imaging
1.9 Multispectral and hyperspectral imaging
1.10 X‐radiographic imaging
1.11 Fluorescence imaging
1.12 Capture of three–dimensional surfaces of art
1.13 Optical coherence tomography (OCT)
1.14 Raman spectroscopic imaging and X‐ray fluorescence imaging
1.15 Summary
1.16 Bibliographical remarks
2 Image processing
2.1 Introduction
2.2 Pixel–based image processing
2.3 Region–based image processing
2.4 Inpainting
2.5 Feature extraction
2.6 Segmentation
2.7 Geometric transformations
2.8 Chamfer transform and Chamfer distance
2.9 Discrete Fourier and wavelet transforms
2.10 Compositing and integrating art images
2.11 Image separation
2.12 Summary
2.13 Bibliographical remarks
3 Color analysis
3.1 Introduction
3.2 Visible–light spectra and color appearance
3.3 Overview of human color vision
3.4 Physics of color in art materials
3.5 Representing color arising from mixing paints
3.6 Digital rejuvenation of pigment colors
3.7 Digital cleaning of paintings
3.8 Summary
3.9 Bibliographical remarks
4 Brush stroke and mark analysis
4.1 Introduction
4.2 Analysis of printed lines and marks
4.3 Inferring tools from marks
4.4 Characterizing the shapes of strokes and marks
4.5 Global methods for inferring sequences of marks in paintings
4.6 Summary
4.7 Bibliographical remarks
5 Perspective and geometric analysis
5.1 Introduction
5.2 Projective geometry
5.3 Estimating the center of projection
5.4 Estimating geometric accuracy in artworks
5.5 Slant anamorphic art
5.6 Inferring depth from projected images
5.7 Summary
5.8 Bibliographical remarks
6 Optical analysis
6.1 Introduction
6.2 Reflection and refraction
6.3 Plane mirrors
6.4 Convex spherical mirrors
6.5 Conical and cylindrical mirrors and anamorphic art
6.6 Concave spherical mirrors
6.7 Converging lenses
6.8 Camera lucida and camera obscura
6.9 Optical projections and the creation of art
6.10 Refraction and nonimaging optics in art
6.11 Summary
6.12 Bibliographical remarks
7 Lighting analysis
7.1 Introduction
7.2 Basic shadows
7.3 Cast–shadow analysis
7.4 Lighting information from highlights
7.5 The optics of diffuse reflections
7.6 Inferring illumination from plane surfaces
7.7 Interreflection
7.8 Occluding–contour algorithms
7.9 Computer graphics for the analysis of lighting
7.10 Shape–from–shading algorithms
7.11 Integrating lighting estimates
7.12 Lighting analysis for dating depicted scenes
7.13 Summary
7.14 Bibliographical remarks
8 Object analysis
8.1 Introduction
8.2 Image–based object classification
8.3 Feature–based analysis of faces and bodies
8.4 Deep neural network–based object recognition
8.5 Summary
8.6 Bibliographical remarks
9 Style and composition analysis
9.1 Introduction
9.2 Automatic classification of style
9.3 Compositional balance
9.4 Geometric properties of composition
9.5 Analysis of trends and similarities in artistic style
9.6 Style transfer
9.7 Recovering Rembrandt's complete
The Night Watch
9.8 Computational generation of images for art analysis
9.9 Summary
9.10 Bibliographical remarks
10 Semantic analysis
10.1 Introduction
10.2 Semantics and visual art
10.3 Meaning through associations
10.4 Semantics of color
10.5 Identifying saints by their attributes
10.6 Learning associations between signifiers and signifieds
10.7 Meaning through artistic style
10.8 Automatic image captioning and question answering
10.9 Meaning through shape relations and associations
10.10 Summary
10.11 Bibliographical remarks
Appendix
A Symbols, acronyms, and mathematical notation
B Probability
C Bayes' theorem and reasoning about uncertainty
D Deep neural networks
E Ray tracing and image formation in mirrors and lenses
F Resources
Bibliographical remarks
Epilog
Glossary
Bibliography
Figure credits
Timeline of artists
Index of artists
Index
About this Book
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Leading image formats used for art images. Although the choice of...
Chapter 2
Table 2.1 Chamfer distances between different copies and the edge map of th...
Chapter 6
Table 6.1 Indices of refraction, , of several common media, where the spee...
Chapter 7
Table 7.1 Comparative lighting analysis of Garth Herrick's paintings in Fig...
Table 7.2 Results of lighting analysis of Johannes Vermeer's
Girl with a Pe
...
Chapter 8
Table 8.1 The mean Euclidian feature distances in three dimensions (
mm
), gi...
Table 8.2 The mean Euclidean feature distances in two dimensions (
mm
), from...
Chapter 9
Table 9.1 Deep net style accuracy, recall, and precision. (Data from
(Lecou
...
Chapter 10
Table 10.1 Several saints frequently depicted in Western Christian art and ...
Appendix
Table A1 Fundamental physical units and symbols and the first page where th...
Table A2 Acronyms used throughout this book and the first page where they a...
Table A3 Mathematical relations and their symbols and the first page where t...
Table A4 Mathematical operations and their notation and the first page where...
Table A5 Symbols and notation from probability and statistics and the first ...
List of Illustrations
Preface
Figure 1 Lorenzo Lotto's
Family Portrait
(also called
Husband and Wife
) (
Figure 2 Morelli's drawings of ears based on the paintings of two Italian ...
Figure 3 Morelli's drawings of hands based on the paintings of two Italian...
Chapter 1
Figure 1.1 A ray of electromagnetic radiation is an oscillating wave of an e...
Figure 1.2 Electromagnetic waves and the continuous spectrum from near ultra...
Figure 1.3 An example plot of the spectral power distribution, showing the r...
Figure 1.4 A broad range of the electro‐magnetic spectrum, showing that the ...
Figure 1.5 The four main layers in a traditional easel painting: the support...
Figure 1.6 The reflectance spectrum of a material describes the reflectivity...
Figure 1.7 Incident electromagnetic radiation with a particular spectrum (up...
Figure 1.8 (
T
) The Bayer pattern in a color filter array (CFA), where a sing...
Figure 1.9 Hasselblad H6D‐100c medium format DSLR (digital single–lens refle...
Figure 1.10 Flatbed scanner for two–dimensional artworks. The scanning head ...
Figure 1.11 Billy Pappas'
Marilyn Monroe
(), graphite on paper (2003). (Her...
Figure 1.12 Details of Billy Pappas'
Marilyn Monroe
of Fig. 1.11.
Figure 1.13 Detail of Billy Pappas'
Marilyn Monroe
(approx. ). The blue sca...
Figure 1.14 A detail from Fig. 1.11 at different spatial resolutions, each a...
Figure 1.15 The bit depth, , determines the number of graylevels in a digit...
Figure 1.16 A passage from Fig. 1.11 rendered with different numbers of gray...
Figure 1.17 A schematic response of a digital sensor, displayed on a log‐log...
Figure 1.18 A standard
color chart
(or sometimes
color checker
), frequently ...
Figure 1.19 Leonardo's
La Bella Principessa
(), trois crayons (black, red, ...
Figure 1.20 Detail of Leonardo's
La Bella Principessa
(approx. ). Notice th...
Figure 1.21 A detail of Leonardo's
La Bella Principessa
(approx. ), showing...
Figure 1.22 Jean‐Auguste‐Dominique Ingres'
Martyrdom of Saint Symphorien
()...
Figure 1.23 Idealized transmission functions of hyperspectral filters of t...
Figure 1.24 Full color and 15 narrow–band hyperspectral scans, centered on t...
Figure 1.25 Data cube of van Gogh's
Bedroom in Arles
. The red line links the...
Figure 1.26 Spectrum at a single point on the baseboard in
Bedroom in Arles
....
Figure 1.27 Facing pages from the
Archimedes Palimpsest
(each double page ap...
Figure 1.28 A portable x‐ray scanner for art works. The source emits a fan o...
Figure 1.29 X‐ray of a detail of Jan van Eyck's
Portrait of Arnolfini and hi
...
Figure 1.30 X‐ray image of detail (approx. ) of Lorenzo Lotto's
Figure 1.31 Perugino's
Adoration of the Magi
(approx. ), fresco (c. 1522–23...
Figure 1.32 The depths of penetration into materials, such as a painting, di...
Figure 1.33 In raking or grazing incidence illumination the artwork is illum...
Figure 1.34 A schematic closeup of craquelure in a painting under raking ill...
Figure 1.35 The three–dimensional structure throughout a detail of Johannes ...
Figure 1.36 Damage to a painting, including impact or an
insult
, is frequent...
Figure 1.37 In reflectance transformation imaging the camera is oriented per...
Figure 1.38 A schematic representation of the physics and optics underlying ...
Figure 1.39 A schematic, exaggerated illustration of RTI. (
L
) The normals, c...
Figure 1.40 Three–dimensional surfaces computed from the same RTI data of an...
Figure 1.41 (
T
) A self portrait by Rembrandt is illuminated normally and cap...
Figure 1.42 A three–dimensional printed copy of a painting by Vincent van Go...
Figure 1.43 (
L
) A schematic ray–tracing diagram for optical coherence tomogr...
Figure 1.44 The sub–layers of varnish on a 17th‐century historical oil paint...
Figure 1.45 (
L
) Attributed to Pierre‐Auguste Renoir,
Boats on the Seine at A
...
Chapter 2
Figure 2.1 Paula von Pausinger's
Ergolet
(), pencil on paper (c. 1920s). Th...
Figure 2.2 X‐ray of a passage in Lorenzo Lotto's
Husband and Wife
of Figs. 1...
Figure 2.3 The pixel–based gamma adjustment , with the values of listed a...
Figure 2.4 The original drawing from Fig. 2.1 is in the center column (); t...
Figure 2.5 One use of the term “contrast” is to describe the
slope
of the tr...
Figure 2.6 The indices of a square support. Only the values of pixels within...
Figure 2.7 Three equivalent representations of the same kernel (full set of ...
Figure 2.8 A radially symmetric filter and three orientated spatial filters,...
Figure 2.9 Paula von Pausinger's
Ergolet
of Fig. 2.1 rendered at pixels, c...
Figure 2.10 Binarized versions of Paula von Pausinger's
Ergolet
for two valu...
Figure 2.11 (
T
) Paula von Pausinger's
Ergolet
of Figs. 2.1, 2.4, and 2.9 (at...
Figure 2.12 The CIE chromaticity diagram with the colors of pixels in a di...
Figure 2.13 Ralph Balson's
Painting number 9
(), synthetic polymer paint on...
Figure 2.14 A detail of Ralph Balson's
Painting number 9
and renderings usin...
Figure 2.15 Pixels corresponding to the dominant (most represented) color fr...
Figure 2.16 The effect of scale on edge extraction, as applied to Johannes V...
Figure 2.17 The original design, based on George Stubbs'
Whistlejacket
, is a...
Figure 2.18 Skeletonization of the region defined by the body of the horse i...
Figure 2.19 Circle–based skeletonization is computed by placing small circle...
Figure 2.20 A detail of Paula von Pausinger's
Woodland study
, before conserv...
Figure 2.21 A passage from Paula von Pausinger's
Woodland study
, ...
Figure 2.22 The spatial filter responses or strengths computed at a single p...
Figure 2.23 Scott Fraser's
Three Way Vanitas
(), oil on linen (2006), with ...
Figure 2.24 The pattern of craquelure depends upon the physical properties o...
Figure 2.25
The Assumption of the Virgin
(detail) attributed to António de O...
Figure 2.26 The binarized craquelure of Johannes Vermeer's
Girl with a Pearl
...
Figure 2.27 Craquelure statistics in the passage from Vermeer's
Girl with a
...
Figure 2.28 (
L
) Detail from the Saint John Evangelist panel of Jan and Huber...
Figure 2.29 Jan van der Heyden's
View of Oudezijds Voorburgwal with the Oude
...
Figure 2.30 Detail of Jan van der Heyden's
View of Oudezijds Voorburgwal wit
...
Figure 2.31 This spatial filter, convolved with the binarized van der Heyden...
Figure 2.32 Steps in the image analysis of the brick patterns in Jan van der...
Figure 2.33 Segmentation of Henri Matisse's
The Dance
based on color similar...
Figure 2.34 The SegNet network for image segmentation: Neurons in blue layer...
Figure 2.35 Semantic segmentation of six paintings, where the percentage are...
Figure 2.36 (a) Pierre‐Auguste Renoir's
Portrait of Mademoiselle Iréne Cahen
...
Figure 2.37 (
T
) Five portraits, (
M
) segmentation with a baseline deep networ...
Figure 2.38 The basic affine transforms and their associated transformation ...
Figure 2.39 The composition of affine transformations. This figure should be...
Figure 2.40 Suppose we are given the image at the top, distorting the artwor...
Figure 2.41 The problem of comparing shapes of curves can be illustrated by ...
Figure 2.42 The
Chamfer transform
(or
distance transform
) applied to a curve...
Figure 2.43 Computation of the Chamfer distance between the curve in Fig. 2....
Figure 2.44 (
L
) Jan van Eyck's Albergati study (), silverpoint on prepared ...
Figure 2.45 Lorenzo Lotto's preparatory study drawing for
Husband and Wife
(
Figure 2.46 A pantograph is a simple hinged device for copying and enlarging...
Figure 2.47 A Reductionszirkel is used for copying and enlarging (or reducin...
Figure 2.48 A putative reenactment of the copying of the Albergati study by ...
Figure 2.49 A micrograph of Jan van Eyck's silverpoint sheet reveals pinpric...
Figure 2.50 An episcope, such as hypothesized was used by van Eyck when copy...
Figure 2.51 Jan van Eyck's silverpoint study for the
Portrait of Niccolò Alb
...
Figure 2.52 When the edge maps of the silverpoint study and the f...
Figure 2.53 Renditions of Cardinal Niccolò Albergati: (a) Jan van Eyck's
Car
...
Figure 2.54 Color‐coded Chamfer transform of Jan van Eyck's silverpoint stud...
Figure 2.55 (
L
) A detail of
Marilyn Monroe
of Fig. 1.11 and (
M
) the magnitud...
Figure 2.56 The basis functions for the discrete cosine transform (DCT) on
Figure 2.57 X‐radiograph of (
T
) Johannes Vermeer's
Woman Writing a Letter wi
...
Figure 2.58 The horizontal and vertical canvas threads (warp and weft, respe...
Figure 2.59 Vertical canvas weave patterns from Johannes Vermeer's (
T
)
The A
...
Figure 2.60 Several members of the two–dimensional Haar wavelet basis functi...
Figure 2.61 Wavelet diagram for a detail from the
Ghent Altarpiece
. The deta...
Figure 2.62 A single component image of the van Eyck brothers'
Gh
...
Figure 2.63 Jan and Hubert van Eyck's
The Annunciation
() panel from
The Gh
...
Figure 2.64 The Annunciation back panel from Jan and Hubert van Eyck's
The G
...
Figure 2.65 A deep net‐based superresolution algorithm applied to a passage ...
Chapter 3
Figure 3.1 The electromagnetic spectrum between and , which includes the ...
Figure 3.2 An illumination spectrum represents the
radiant intensity
(amount...
Figure 3.3 An idealized illumination spectrum of white light contains equal ...
Figure 3.4 The relative spectral sensitivities of the three cone types in no...
Figure 3.5 The most important molecule subserving vision in mammals is Rhodo...
Figure 3.6 Color patches differing in hue, in saturation, and in lightness....
Figure 3.7 Many three‐dimensional color spaces display lightness vertically ...
Figure 3.8 (
L
) Colors organized by the properties of hue, saturation, and li...
Figure 3.9 The neural signals from the short–, intermediate–, and long–wavel...
Figure 3.10 Hues can be arranged in a circle and spaced such that additive c...
Figure 3.11 Demonstration of simultaneous contrast, inspired by the demonstr...
Figure 3.12 The 1931 CIE chromaticity diagram. Monochromatic colors lie arou...
Figure 3.13 Here the color has chromaticities , which corresponds to domi...
Figure 3.14 When two colors, here and , are mixed additively by proportio...
Figure 3.15 Closeup of color television screen showing red, green, and blue ...
Figure 3.16 The chromaticity coordinates of numerous points selected from th...
Figure 3.17 Vincent van Gogh's color palette during three stages in his care...
Figure 3.18 A molecule of orange pigment, , is rather large, as are most na...
Figure 3.19 Reflectance spectra between and of several common artists' p...
Figure 3.20 The color appearance of an applied paint depends upon a number o...
Figure 3.21 A schematic closeup of International Klein Blue pigment reveals ...
Figure 3.22 Vantablack nanotubes have walls one atom thick. Each tube is rou...
Figure 3.23 The results from mixing two particular pigments having the chrom...
Figure 3.24 Guido Reni's
Immaculate Conception
(), oil on canvas (1627), Me...
Figure 3.25 Three details from Johannes Vermeer's
Girl with a Pearl Earring
...
Figure 3.26 Panel Five of Mark Rothko's
Harvard Mural
(), egg tempera and d...
Figure 3.27 Detail of an oil painting (approx. ) when the portion behind th...
Figure 3.28 Georges Seurat's
Sunday Afternoon on the Island of La Grande Jat
...
Figure 3.29 Digital or virtual rejuvenation of the passage (approx. ) above...
Figure 3.30 A schematic of the conditions relevant to virtual or digital cle...
Figure 3.31 A detail from an oil painting during cleaning by a conservationi...
Figure 3.32 Spectra measured and estimated in a small blue sky pa...
Figure 3.33 Leonardo's
Mona Lisa
(), oil on poplar panel (c. 1503–06), (
L
) ...
Chapter 4
Figure 4.1 Cy Twombly's
Untitled
(), pencil, wax crayon, oil‐based paint, a...
Figure 4.2 Detail of Cy Twombly's
Untitled
of Fig. 4.1, ().
Figure 4.3 Detail of Buddhist thanka from Nepal (approx. ), paint on paper ...
Figure 4.4 Steps in traditional monochrome woodblock printing in the West. T...
Figure 4.5 The usage and wear of a wood keyblock leads to widening of printe...
Figure 4.6 (
L
) Katsushika Hokusai's
The Pink Fuji
, also called
Fine Wind, Cl
...
Figure 4.7 Details from Katsushika Hokusai's (
L
)
The Pink Fuji
, and (
R
)
The
...
Figure 4.8 Schematic pine trees in Hokusai's (
L
)
The Pink Fuji
, and (
R
)
The
...
Figure 4.9 Steps in copperplate etching: The artist uses a needle or
pin
to ...
Figure 4.10 A line printed in the first edition of a copperplate run (left) ...
Figure 4.11 Rembrandt's
Portrait of the Artist as a Young Man
(), etching (...
Figure 4.12 The progressive thinning of the same engraved lines in successiv...
Figure 4.13 The red and blue pixels are the skeletons, or medial axis transf...
Figure 4.14 The line width and date of publication in copies of Porcacchi'...
Figure 4.15 Sheila Waters'
Tor House
(poem by Robinson Jeffers) (), written...
Figure 4.16 Details of Sheila Waters'
Tor House
of Fig. 4.15 (eac...
Figure 4.17 Representative marks made with the following tools: (a) horse–ha...
Figure 4.18 Boundary contours made by thresholding high–resolution images of...
Figure 4.19 The parts of a traditional paintbrush for easel painting: the ha...
Figure 4.20 A range of tools (brushes) often used by easel painters working ...
Figure 4.21 Extracted brush strokes from Vincent van Gogh's
Red Cabbages and
...
Figure 4.22 Normalized histograms of the number of brush strokes in a neighb...
Figure 4.23 Schematic brush strokes to illustrate the problem of brush strok...
Figure 4.24 Vincent van Gogh's
Self Portrait with a Grey Felt Hat
(), oil o...
Figure 4.25 Successive states of the digital removal of layers of brush stro...
Figure 4.26 Jackson Pollock's
Lucifer
(detail) with marks removed by a modif...
Figure 4.27 Jackson Pollock's
Lucifer
(), oil and enamel on canvas (1947), ...
Figure 4.28 (
T
) A schematic of a yellow watercolor brush stroke overlapping ...
Figure 4.29 Rosemåling floral design, oil on wood (20th century), artist unk...
Figure 4.30 The colors that result from overlapping semi–transparent strokes...
Figure 4.31 Schematic overlap of three semi–transparent brush strokes of col...
Figure 4.32 The color layers of the rosemåling pattern in Fig. 4.29 extracte...
Figure 4.33 The four color layers in the rosemåling design computed from the...
Figure 4.34 (
L
) Paul Klee's
Architecture of the Plain
(), watercolor and pe...
Figure 4.35 After Henri Matisse's
Woman with Loose Hair
(), pen and ink on ...
Figure 4.36 (
T
) Two crossing pen marks and associated skeletons computed by ...
Figure 4.37 A curve, such as a pen stroke in the upper–right panel, can be r...
Figure 4.38 Estimates of the development of Vincent van Gogh's
Wheat Field w
...
Chapter 5
Figure 5.1 Fra Carnevale's
The Ideal City
(), oil and tempera on panel (148...
Figure 5.2 The projection of a three–dimensional object onto a two–dimension...
Figure 5.3 There is an inherent ambiguity due to geometric projections of a ...
Figure 5.4 There are infinitely many three–dimensional geometric figures tha...
Figure 5.5 The equivalence between Alberti's window and a pinhole camera mod...
Figure 5.6 The projection setup of Fig. 5.5, viewed from the side, with the ...
Figure 5.7 The projection of a point with coordinates in the scene to ...
Figure 5.8 (
T
) Basic perspective projection of a grid on a plane showing ort...
Figure 5.9 A cube rendered in (
T
) accelerated perspective, in which the cent...
Figure 5.10 The effect of the location of the center of projection upon the ...
Figure 5.11 An overhead view of an artwork in a gallery and the center of pr...
Figure 5.12 One–, two‐, and three–point perspective describes the number of ...
Figure 5.13 Ryūjo (Tatsujo)
The Tale of Genji
, hand scroll, ink and color on...
Figure 5.14 Geometry of projection of a cube, showing distant points. The li...
Figure 5.15 If the right and left distant points are due to lines at in th...
Figure 5.16 Geometry for deriving the locations for which the distant points...
Figure 5.17 This is an overhead view of the wall of a gallery where the sepa...
Figure 5.18 (
T
) A frontal view of Fra Carnevale's
The Ideal City
...
Figure 5.19 Computer graphics model of the architecture in Gustave Caillebot...
Figure 5.20 A portion of a map of Paris, just north of the Place de l'Europe...
Figure 5.21 Stacked presentation of paintings in the Carnegie Art Museum, Pi...
Figure 5.22 Fra Filippo Lippi's
Saint Lawrence Enthroned with Saints and Don
...
Figure 5.23 Comparing heights of pillars in a perspective image. Two pillars...
Figure 5.24 Piero della Francesca's
Flagellation of Christ
(), oil and temp...
Figure 5.25 Comparing intrinsic heights in Piero della Francesca's
Flagellat
...
Figure 5.26 Bartholomeus van Bassen's
Interior of a Catholic Church
(), oil...
Figure 5.27 Finding the center of projection based on a projected image and ...
Figure 5.28 Perspective scheme of Hans Memling's
Flower Still‐Life
(or...
Figure 5.29 A perspective transformation of the front half of the carpet in ...
Figure 5.30 Lorenzo Lotto's
Husband and Wife
perspective analysis. Such asym...
Figure 5.31 A homography describes a projection mapping from points in one p...
Figure 5.32 The residuals to be minimized when estimating a homography betwe...
Figure 5.33 Jan van Eyck's
Portrait of Giovanni Arnolfini and his Wife
(), ...
Figure 5.34 The orthogonals defined by the floor of the
Arnolfini Portrait
a...
Figure 5.35 Arnolfini chandelier perspective analysis: (
T
) overhead view (pl...
Figure 5.36 Detail of Jan van Eyck's
Portrait of Giovanni Arnolfini and his
...
Figure 5.37 A typical 14th‐century chandelier design from northern Europe il...
Figure 5.38 A prayer book holder contemporaneous with the Arnolfini chandeli...
Figure 5.39 Top of a 15th‐century prayer book holder, with digitally added m...
Figure 5.40 Perspective test of Arnolfini chandelier with candidate vanishin...
Figure 5.41 Arnolfini arms
6
and
1
transformed by the optimal homography (ba...
Figure 5.42 The chandelier in the
Arnolfini Portrait
and Nicholas C. William...
Figure 5.43 Two arms from Nicholas C. Williams'
Chandelier II
, segmente...
Figure 5.44 (
L
) Andrea Mantegna's
Lamentation of Christ
(), tempera on canv...
Figure 5.45 A schematic siting of murals on the barrel ceiling of Sennedjem'...
Figure 5.46 (
T
) The original two murals from the barrel vault in Sennedjem's...
Figure 5.47 Full wall murals of Sennedjem's Tomb, where the barrel vaults we...
Figure 5.48 (
L
) Giorgio de Chirico's
Ariadne
(), oil and graphite on canvas...
Figure 5.49 Robert Campin and workshop's
Mérode Altarpiece
(
Annunciatio
...
Figure 5.50 Perspective scheme of
The Mérode Altarpiece
. The vanishing ...
Figure 5.51 A detail from the right panel of the
Mérode Altarpiece
, app...
Figure 5.52 The trellis in the
Mérode Altarpiece
compressed to better r...
Figure 5.53
The Mérode Altarpiece
trellis compressed to bett...
Figure 5.54 The slats of the
Mérode
trellis extracted and aligned to re...
Figure 5.55 Ed Ruscha's
Baby Doe Soapy Smith
(), acrylic paint on paper (19...
Figure 5.56 Ed Ruscha's
Baby Doe Soapy Smith
transformed by an affine scale ...
Figure 5.57 Slant anamorphic art can be created by means of a transformed gr...
Figure 5.58 An undistorted detail from the
Ghent Altarpiece
and superimposed...
Figure 5.59 A computational slant anamorphic warping of the detail in Fig. 5...
Figure 5.60 Hans Holbein's
The Ambassadors
(), oil on oak panel (1533), Nat...
Figure 5.61 Masaccio's
The Holy Trinity with the Virgin and Saint John and D
...
Figure 5.62 Views of a three–dimensional model computed from Masaccio's
The
...
Figure 5.63 The three–dimensional location of a point can be computed from...
Figure 5.64 Scott Fraser's
Three Way Vanitas
(), oil on linen (2006).
Figure 5.65 A diagram of the three–dimensional tableau of Scott Fraser's
Thr
...
Figure 5.66 The effective views of the tableau in Scott Fraser's
Three Way V
...
Figure 5.67 The depth of objects in the tableau of Scott Fraser's
Three Way
...
Chapter 6
Figure 6.1 In specular or mirror–like reflection a light ray obeys the law o...
Figure 6.2 The law of refraction, or Snell's Law (Eq. 6.2), relates the angl...
Figure 6.3 Refraction by water leads to a visual displacement or shift in th...
Figure 6.4 Heather Horton's
Hannah, Flying
(), oil on panel (2012), shows t...
Figure 6.5 A single ray leaves a point on an object (tip of the green arro...
Figure 6.6 Light leaves the tip of an object (green arrow at the left), , a...
Figure 6.7 A side view of the ray–tracing diagram in Fig. 6.6. The rays from...
Figure 6.8 A plane mirror produces a virtual image of the hand that is mirro...
Figure 6.9 A man stands the object distance, , from a plane mirror and view...
Figure 6.10 Charles C. Hofmann's
Montgomery County Almshouse
(), oil on can...
Figure 6.11 Katsushika Hokusai's
Fuji Reflection in Lake at Misaka in Kai Pr
...
Figure 6.12 René Magritte's
Not to be Reproduced
(), oil on canvas (1937). ...
Figure 6.13 Diego Velázquez's
Las Meninas
(), oil on canvas (1656), Museo d...
Figure 6.14 Computer graphics reconstruction of Diego Velázquez's
Las Menina
...
Figure 6.15 Computer graphics reconstruction of
Las Meninas
: (
L
) view from a...
Figure 6.16 Virtual tableau with double portrait consistent with the mirror ...
Figure 6.17 Light rays propagating parallel to and near the axis strike the ...
Figure 6.18 The facial diameter, , is the size of a convex mirror; its radi...
Figure 6.19 Two convex mirrors that have the same facial size, , are viewed...
Figure 6.20 Image formation in a convex mirror. The rays from the tip of the...
Figure 6.21 Scott Fraser's
Four Ornaments
(), oil on panel (2018). The arti...
Figure 6.22 George Lambert's
The Convex Mirror
( diameter), oil with pencil...
Figure 6.23 Detail of Jan van Eyck's
Portrait of Giovanni Arnolfini and his
...
Figure 6.24 A ray from a distant point a distance from the mirror axis str...
Figure 6.25 The dewarping transformation of an image in a convex spherical m...
Figure 6.26 Amnon David Ar's
Self Portrait in a Convex Mirror
(), oil on ca...
Figure 6.27 Transformed images from the Arnolfini mirror based on different ...
Figure 6.28 Perspective analysis of the optimally dewarped image from the Ar...
Figure 6.29 (
L
) An unaltered photograph of a ceiling–mounted spherical secur...
Figure 6.30 A Claude glass (or Claude mirror or occasionally black glass) is...
Figure 6.31 Parmigianino's
Self–Portrait in a Convex Mirror
(‐diamete...
Figure 6.32 Computer graphics model showing Parmigianino in his studio. The ...
Figure 6.33 Computer graphics model of just the walls and window in Parmigia...
Figure 6.34 Final computer graphics model of
Self–Portrait in a Convex Mirro
...
Figure 6.35 (
L
) The proper way to view
Self–Portrait in a Convex Mirror
...
Figure 6.36 Parmigianino's
Self–Portrait in a Convex Mirror
viewed fro...
Figure 6.37 Hans Memling's
Virgin and Child and Maarten van Nieuwenhove
(, ...
Figure 6.38 A computer graphics model showing four configurations of the hea...
Figure 6.39 Candidate dewarpings of the image in the convex mirror in Hans M...
Figure 6.40 Comparison of the best dewarped image of the Virgin with the dir...
Figure 6.41 (
L
) Scott Fraser's
Reflections
(), oil on board (1993), and (
R
)...
Figure 6.42 (
L
) A three–dimensional cylindrically symmetric form (mirror) wi...
Figure 6.43 (
T
) The edge map of Fraser's
Reflections
computed using the edge...
Figure 6.44 A conical anamorphic mirror or
anamorphoscope
is to be placed at...
Figure 6.45 Conical anamorphic painting,
Girl with a Bird on a Wire
, (17th c...
Figure 6.46 (
L
) Rays from the conical anamorphic artwork strike the cone and...
Figure 6.47 Linear anamorphic cone transformation grid. Points on the inside...
Figure 6.48 The optical transformation between the distorted annular anamorp...
Figure 6.49 Gert Dittmers's
Anamorphic Double Portrait of King Frederick III
...
Figure 6.50 (
L
) Ray tracing for a cylindrical anamorphic artwork to be viewe...
Figure 6.51 Grid for cylindrical mirror anamorphic art that surrounds the cy...
Figure 6.52 Gert Dittmers'
Anamorphic Double Portrait of King Frederick III
...
Figure 6.53 Cylindrical anamorphic art transformation. The flat, distorted f...
Figure 6.54 Parallel light rays entering from the left strike a small concav...
Figure 6.55 Paraxial light rays strike a concave mirror and are brought to t...
Figure 6.56 When an object is closer to a concave mirror than the focal poin...
Figure 6.57 Image formation in a concave mirror with the object far from the...
Figure 6.58 A simple converging lens takes rays parallel and near to the axi...
Figure 6.59 Virtual image formation in a thin converging lens: The virtual i...
Figure 6.60 (
T
) Improper and (
B
) proper way to use a magnifying glass to exa...
Figure 6.61 Simple converging lens with focal points and , focal length
Figure 6.62 We find the path of the ray that leaves , passes through the co...
Figure 6.63 (
L
) A ray–tracing diagram of a thin pane of glass (which acts as...
Figure 6.64 A pinhole camera—the small shaded box at the right—consists of a...
Figure 6.65 A simple camera obscura with a single converging lens. Two point...
Figure 6.66 The rays within the camera obscura strike the screen on the rear...
Figure 6.67 The orientation or parity of images of an
R
produced by a conver...
Figure 6.68 The blur spots produced in the camera obscura of Fig. 6.65, at t...
Figure 6.69 (
T
) The images of two ideal points separated above than the Rayl...
Figure 6.70 A blur spot or circle of confusion is an out–of–focus image of a...
Figure 6.71 (
L
) Focusing by a perfect spherical mirror of large facial diame...
Figure 6.72 Wireframe computer graphics model superimposed on the
Arnolfini
...
Figure 6.73 Side view of the computer graphics model of the Arnolfini studio...
Figure 6.74 Putative projection using a concave mirror setup for the Arnofin...
Figure 6.75 Computer graphics model and overhead view of Caravaggio's
Supper
...
Figure 6.76 Ray–tracing diagrams for putative projectors in Caravaggio's
Sup
...
Figure 6.77 Putative projector setup, with no screen present, as proposed in...
Figure 6.78 Computer ray–tracing diagram of the proposed concave‐mirror proj...
Figure 6.79 Blur spots of nearby objects (below) are in focus and of farther...
Figure 6.80 Putative projector setup that includes the ‐‐wide canvas of
Hu
...
Figure 6.81 Schematic ray–tracing diagram of the projector in Fig. 6.80, whi...
Figure 6.82 The blur spots in the putative projector in the realistic (off a...
Figure 6.83 (
L
) Inferred positions of camera obscura lenses and associated v...
Figure 6.84 Jenison's mirror comparator design is a telescope, similar to, b...
Figure 6.85 Computer graphics rendering after Vermeer's
Lady at the Virginal
...
Figure 6.86 Photographer Hiroshi Sugimoto's
The Music Lesson
(after Vermeer)...
Figure 6.87 Matthew Grabelsky's
Seated Figure Study
(), charcoal on paper (...
Figure 6.88 Modern studio setup of Johannes Vermeer's
Lady at the virginals
....
Figure 6.89 Details from four paintings showing luminance gradients on rear ...
Figure 6.90 The red arrows show the slightly bowed horizontal contour in Ver...
Figure 6.91 Canaletto's
Piazza San Marco
(), oil on canvas (late 1720s), Me...
Figure 6.92 Canaletto's
Piazza San Marco
perspective scheme. The buildings t...
Figure 6.93 Philip Barlow's
glide II
(), oil on canvas (2015).
Figure 6.94 Detail of
glide II
(approximately ), showing the blur spots and...
Figure 6.95 Attributed to Leonardo da Vinci,
Salvator Mundi
(), oil on pane...
Figure 6.96 Cutaway view of a solid sphere (one model for the orb in
Salvato
...
Figure 6.97 Ray tracing in hollow and solid crystal orbs, as may have been u...
Figure 6.98 Computer graphics renderings of
Salvator Mundi
, attributed to Le...
Figure 6.99 Slight alterations in the hand position lead to significantly di...
Chapter 7
Figure 7.1 “Rembrandt portrait lighting” typically consists of a single sour...
Figure 7.2 The two major classes of shadows are
cast shadows
(onto a separat...
Figure 7.3 A light source illuminates a sphere (occluder) lying on a plane (...
Figure 7.4 The angular size of the illumination source determines the size o...
Figure 7.5 A shadow painting surrounding an epitaph from 1632 in the Ringsak...
Figure 7.6 Johannes Vermeer's
Girl with a Pearl Earring
(), oil on canvas (...
Figure 7.7 Cast–shadow analysis based on the nose in Johannes Vermeer's
Girl
...
Figure 7.8 Frederic Edwin Church's
Sunset Jamaica
(), oil on paper mounted ...
Figure 7.9 Cast shadows of two vertical posts onto a plane. Even though only...
Figure 7.10 We can infer the position of the point‐source illuminant from th...
Figure 7.11 The specularity of a surface describes the relative intensities ...
Figure 7.12 The light leaving source , reflecting from the object (red sphe...
Figure 7.13 The specular reflection or highlight of a small illumination sou...
Figure 7.14 The red circles marking the
limbus
(outer boundary of the iris) ...
Figure 7.15 The human eyeball has a cornea (highlighted in light yellow), wh...
Figure 7.16 The direction of gaze can be estimated from the orientation and ...
Figure 7.17 The image of a circle (such as the edge of an iris on the right ...
Figure 7.18 A cutaway view of a computer graphics model of the pearl in
Girl
...
Figure 7.19 The wireframe computer graphics model is derived from points loc...
Figure 7.20 When an incident light ray (blue arrow) strikes the surface of a...
Figure 7.21 Lambert's cosine law: A surface with illumination from a distant...
Figure 7.22 Lambert's cosine law describes the relative amount of light refl...
Figure 7.23 The illumination of a plane surface by a point source. Here ,
Figure 7.24 The location of the point‐source illuminant inferred from the pa...
Figure 7.25 (
L
) Bust with full set of normals. In general, we do not know th...
Figure 7.26 Johannes Vermeer's
Girl with a Pearl Earring
with automatic edge...
Figure 7.27 (
L
) The sphere is illuminated by a distant point source from . ...
Figure 7.28 The single–point occluding–contour algorithm is simply to find t...
Figure 7.29 The general occluding–contour algorithm applied to Georges de la...
Figure 7.30 Johannes Vermeer's
Girl with a Pearl Earring
with occluding cont...
Figure 7.31 The general occluding–contour algorithm applied to (
L
) Caravaggi...
Figure 7.32 Portraitist Garth Herrick in his studio, working from photograph...
Figure 7.33 (
L
) Photographic referents of the background, subject, and (arti...
Figure 7.34 The geometry and variables used in lightfield occluding–contour ...
Figure 7.35 The five principal real spherical harmonics used to describe the...
Figure 7.36 (
T
) Five spherical harmonics basis functions, as projected onto ...
Figure 7.37 Caravaggio's
Adoration of the Shepherds
(), oil on canvas (1609...
Figure 7.38 Measured intensities along contours in Caravaggio's
Adoration of
...
Figure 7.39 Garth Herrick's
Apotheoun
() (2004) and
Human on my Faithless A
...
Figure 7.40 Frederic Remington's
The Thunder–Fighters would take their Bows
...
Figure 7.41 Frederic Remington's
He Rushed the Pony right to the
...
Figure 7.42 Wireframe model of Georges de la Tour's
Christ in the
...
Figure 7.43 Side and overhead (plan) views of a wireframe model of Georges d...
Figure 7.44 Computer graphics model of Georges de la Tour's
Chris
...
Figure 7.45 Comparison of two candidate positions for the illuminant in
Chri
...
Figure 7.46 Different views of a computer graphics model of Vermeer's
Girl w
...
Figure 7.47 The computer graphics model of Vermeer's
Girl with a Pearl Earri
...
Figure 7.48 Computer graphics model of René Magritte's
The Menaced Assassin
...
Figure 7.49 A single light ray enters from the right at the angle of inciden...
Figure 7.50 (
L
) Computer graphics model of Caravaggio's
The Calling of St. M
...
Figure 7.51 There is always ambiguity in shape from shading, here with the h...
Figure 7.52 The shape–from–shading problem is: given a two–dimensional shade...
Figure 7.53 Four small regions (such as pixels) of different brightness in a...
Figure 7.54 Heather Horton's
I will not Jettison my Dreams
(), oil on panel...
Figure 7.55 A detail of Heather Horton's
I will not Jettison my Dreams
in Fi...
Figure 7.56 Vermeer albedo with scaled and oriented generic three–dimensiona...
Figure 7.57 Vermeer albedo estimates and computed through shape–from–sha...
Figure 7.58 A schematic diagram of the progress of the generalized expectati...
Figure 7.59 Integration of Vermeer lighting estimates. Each Gaussian curve r...
Figure 7.60 The summary of seven results of the lighting estimation for the ...
Figure 7.61 The estimate of the direction to the incident light (for instanc...
Figure 7.62 The integration of estimates of illumination direction from thre...
Figure 7.63 One benefit of representing estimates probabilistically is that ...
Figure 7.64 Georges de la Tour's
Christ in the Carpenter's Studio
with s...
Figure 7.65 Johannes Vermeer's
View of Delft
(), oil on canvas (1659–1660)....
Figure 7.66 (
L
) Detail of Johannes Vermeer's
View of Delft
(approx. ), show...
Figure 7.67 (
L
) Modern map of the central portion of Delft. Some of the coas...
Chapter 8
Figure 8.1 Feature locations computed for two faces in representational pain...
Figure 8.2 Different classes of feature points computed in a detail of
Maril
...
Figure 8.3 Four of the most‐securely established contemporary portraits of L...
Figure 8.4 Farkas feature points comprise a compressed representation and ca...
Figure 8.5 Four candidate portraits of young or middle–aged Leonardo: a) Ver...
Figure 8.6 A schematic illustration of just three of the many dimensions def...
Figure 8.7 A three–dimensional morphable model of a human face with differen...
Figure 8.8 The first and second columns show candidate portraits of Leonardo...
Figure 8.9 Histograms of the within‐group feature distances (blue) and inter...
Figure 8.10 A graph, embedded in two dimensions, of the Farkas similarities ...
Figure 8.11 (
L
) Titian's
Salomé with the Head of John the Baptist
(), ...
Figure 8.12 Computed interpose distances can be represented by a graph—here ...
Figure 8.13 The pose of a portrait head can be described by rotation angles ...
Figure 8.14 Schematic showing the method for estimating head pose (roll, pit...
Figure 8.15 A box–whisker plot of the absolute value of the roll angle of po...
Figure 8.16 A box–whisker plot of the distribution of the proportion of huma...
Figure 8.17 Jacques‐Louis David's
Oath of the Horatii
. The yellow bounding b...
Figure 8.18 Faces found by a trained deep net applied to a large corpus of p...
Figure 8.19 The left column shows two query images presented to a deep netwo...
Chapter 9
Figure 9.1 The classification confusion matrix for a deep net trained to ide...
Figure 9.2 The left panel shows a portrait in the style of Rembrandt, presen...
Figure 9.3 The distribution of lightness barycenters for several genuine Rem...
Figure 9.4 Pollaiuolo's
Martyrdom of Saint Sebastian
() oil on wood (1475)....
Figure 9.5 Pollaiuolo's
Martyrdom of Saint Sebastian
with computed figure sk...
Figure 9.6 Piet Mondrian's
Composition II with Red, Blue and Yellow
(), oil...
Figure 9.7 The central panel is a computer‐rendered approximation to Mondria...
Figure 9.8 (a)
Composition with large Blue plane, Red, Black, Yellow, and Gr
...
Figure 9.9 Digital renderings of “earlier state” (es) works by Mondrian, tha...
Figure 9.10 A hidden Markov model for generating faux Neoplastic paintings b...
Figure 9.11 The development of a faux Mondrian, generated by a hidden Markov...
Figure 9.12 Faux Mondrian designs generated by a hidden Markov model trained...
Figure 9.13 The chromatic entropy , measured in bits, is a quantitative mea...
Figure 9.14 Vincent van Gogh's
The Harvest at La Crau
rendered at very low s...
Figure 9.15 Claude Lorrain's
Seaport with the Embarkation of the Queen of Sh
...
Figure 9.16 Histograms of the entropy reduction, in bits, for 14,600 landsca...
Figure 9.17 A two–dimensional latent representation within a classification ...
Figure 9.18 A similarity graph showing strong similarities in palette and co...
Figure 9.19 Portrait photograph—the “content” image—and resulting image afte...
Figure 9.20 (
L
) Raphael's
Miraculous Draught of Fishes
cartoon (), tempera ...
Figure 9.21 Gustav Klimt's
Medicine
ceiling painting (c. 1900), (
L
) photogra...
Figure 9.22 (a) The computed edge map of Leonardo's
Madonna of the Carnation
Figure 9.23 (a) Pablo Picasso's
The Crouching Beggar
(), oil on canvas (190...
Figure 9.24 (a) Vincent van Gogh
Still Life with Meadow Flowers and Roses
(
Figure 9.25 Rembrandt's
The Company of Captain Banning Cocq and Lieutenant W
...
Figure 9.26 Gerrit Lundens'
The Company of Captain Banning Cocq and Lieutena
...
Figure 9.27 The arrows mark the displacements between corresponding feature ...
Figure 9.28 Rembrandt's
The Night Watch
, at its full dimensions, with border...
Figure 9.29 This faux Rembrandt portrait was created entirely algorithmicall...
Figure 9.30 Proof–of–concept computational reconstruction of Diego Velázquez...
Chapter 10
Figure 10.1 Jacques‐Louis David's
Oath of the Horatii
(), oil on canvas (17...
Figure 10.2 A small portion of a hierarchical ontology, based on the relatio...
Figure 10.3 Marnius van Reymerswaele's
Saint Jerome in his Study
(), oil on...
Figure 10.4 (
L
) Correggio's
Madonna and Child with Saints Jerome and Mary Ma
...
Figure 10.5 (a) Unknown artist's
Stefani Triptych, Saint Peter enthroned
(c....
Figure 10.6 (
L
) Images of keys culled from Western artwork from the 13th thr...
Figure 10.7 The output of the attribute recognition processing stage, here a...
Figure 10.8 (
L
) Andrea del Verrocchio's
Baptism of Christ
(), oil on wood (...
Figure 10.9 Harmen Steenwijck's
Still Life: An Allegory of the Vanities of H
...
Figure 10.10 A knowledge graph learned from automated natural language proce...
Figure 10.11 Roy Lichtenstein's
Little Big Painting
(), oil and acrylic on ...
Figure 10.12 Pierre‐Auguste Renoir's
Luncheon of the Boating Party
(), oil ...
Figure 10.13 Rogier van der Weyden's
Descent from the Cross
(), oil on pane...
Figure 10.14 Skeletonization of Christ and Mary reveals very similar posture...
Figure 10.15 Albrecht Dürer's
Adam and Eve
(), engraving (1504). The story ...
Appendix
Figure A1 (
L
) The scalar or dot product of two vectors is . (
R
) The cross p...
Figure A2 The two–dimensional surface illustrates the function , and the bl...
Figure A3 The sum of four discrete cosine functions (from the basis function...
Figure A4 The magnitude of the lowest–order spherical harmonic basis functio...
Figure A5 The Law of Total Probability applied to a discrete distribution. T...
Figure A6 The area under a continuous probability distribution, , is 1.0.
Figure A7 A two–dimensional discrete probability distribution. The Law of To...
Figure A8 A two–dimensional probability density function. The Law of Total P...
Figure A9 The conditional probability density function, for the value ma...
Figure A10 A simple hidden Markov model consisting of
ST
and
end
states and ...
Figure A11 (
T
) The data set of eight data points in one dimension, and can...
Figure A12 Integration of two–dimensional estimates by maximum likelihood. T...
Figure A13 The bias and variance of an estimate describes the overall error ...
Figure A14 The metric quantifies the quality of match between two regions,...
Figure A15 A full deep neural network architecture, where the input layer is...
Figure A16 A small portion of a deep neural network, showing a few neurons i...
Figure A17 (
L
) Basic converging and (
R
) diverging lenses on an optical axis....
Figure A18 Ray tracing in a converging lens, showing image formation. The th...
Figure A19 Ray tracing in a converging lens with the object closer to the le...
Figure A20 Ray tracing in a diverging lens. The three principal rays are sho...
Figure A21 Ray tracing and image formation in a concave mirror for an object...
Figure A22 A paraxial ray (Principal Ray
1
), parallel to the axis, strikes a...
Figure A23 An ideal parabolic concave mirror takes parallel rays along the a...
Guide
Cover
Table of Contents
Title Page
Copyright
Dedication
List of Figures
List of Tables
List of Algorithms
Preface
Begin Reading
Appendix
Epilog
Glossary
Bibliography
Figure credits
Timeline of artists
Index of artists
Index
End User License Agreement
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PIXELS & PAINTINGS
FOUNDATIONS OF COMPUTER‐ASSISTED CONNOISSEURSHIP
DAVID G. STORK
Stanford University
CA, USA
Copyright © 2024 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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