`Generation of anaglyph stereoscopic imagesEric DuboisToday's Program· · · · · · · Generalities on stereoscopic viewing What is anaglyph? Mathematical formulation of color stereo viewing Mathematical formulation of anaglyph viewing Method to generate anaglyphs by projection Some results What's left?June 14, 2000Eric Dubois2Stereoscopic image transmission and viewingJune 14, 2000Eric Dubois3Stereoscopic Pair (Ray Hannisian)June 14, 2000Eric Dubois4Stereoscopic display methods· · · · · Stereoscope (1832) Anaglyph (1853) Polarized glasses (1891) Liquid crystal shutter (time-sequential) Autostereoscopic (no glasses)June 14, 2000Eric Dubois5Wheatstone's stereoscopeJune 14, 2000Eric Dubois6Stereoscope opticsJune 14, 2000Eric Dubois7Polarized stereoscopic displayJune 14, 2000Eric Dubois8What is `anaglyph'?Anaglyph is a method to view stereoscopic images using colored spectacles. The method was patented in 1891 by Louis Ducos du Hauron, but similar methods had been demonstrated previously by W. Rollmann in 1853 and J.C. D'Almeida in 1858.June 14, 2000Eric Dubois9Origin of the word anaglyphThe word anaglyph is from the Greek  == again µ == sculptureJune 14, 2000Eric Dubois10Classical methodFor monochrome stereo images, the left view in blue (or green) is superimposed on the same image with the right view in red. When viewed through spectacles of corresponding colors but reversed, the three-dimensional effect is perceived.June 14, 2000Eric Dubois113D drawingJune 14, 2000Eric Dubois12Bubbles (André-Claude Latulippe)June 14, 2000Eric Dubois13Dinosaur (Henry Chung)June 14, 2000Eric Dubois14Ideal Stereoscopic Display· Input left and right views:' Vlj' (x),Vrj (x), j = 1,2,3; x L· The three components j=1,2,3 are gamma-corrected RGB (in that order) that can be directly displayed by a standard RGB display. · L is the sampling raster for the imageJune 14, 2000Eric Dubois15Ideal Stereoscopic Display· The three components go through the display gamma, denoted g, and excite the display RGB phosphors,V j (x ) = g V 'j (x ) ,  = l , r ; j = 1,2,3()· The spectral density functions of the RGB display phosphors are denoted d j ( ), j = 1,2,3 · The light emanating from point x in left and right images is given by 3 Ql ( , x ) =  Vlj (x )d j ( )j =1 3Qr ( , x ) =  Vrj (x )d j ( )j =1June 14, 2000Eric Dubois16June 14, 2000Eric Dubois17Perceived stereo pair· The color perceived at point x in the left and right images is determined by the projection of Ql( ,x) and Qr( ,x) onto the visual subspace using color matching functions pk ( )~ Vlk (x ) =  Ql ( , x )pk ( )d =  Vlj (x ) pk ( )d j ( )dj =1 3 3=  ckjVlj (x ), k = 1,2,3j =1June 14, 2000Eric Dubois18Perceived stereo pair~ Vl (x ) = CVl (x ) · In matrix notation,[C]kj = ckj =  pk ( )d j ( )d· Similarly, · With the standard XYZ color space, 0.4641 0.3055 0.1808 C = 0.2597 0.6592 0.0811   0.0357 0.1421 0.9109  June 14, 2000~ Vr (x ) = CVr (x )Eric Dubois19Perceived Stereo Image· The value of the stereo image at each point x can be considered to be an element of a sixdimensional vector space S6~  Vl1 (x )  ~  Vl 2 (x ) ~ Vl 3 (x ) ~ V (x ) =  ~  Vr1 (x )  ~ Vr 2 (x ) ~  Vr 3 (x )June 14, 2000Eric Dubois20Visualization of an Anaglyph Image· The anaglyph image is denoted' Vaj (x ), j = 1,2,3; x L· The light emitted from the screen at point x isQa ( , x ) =  Vaj (x )d j ( )j =1 ' · where Vaj (x ) = g (Vaj (x )) 3June 14, 2000Eric Dubois21Anaglyph ImageJune 14, 2000Eric Dubois22Perceived Anaglyph Image with Glasses· The light from the CRT passes through two filters with spectral absorption functions fl() and fr() before arriving at the left and right eyes. · The light spectral density at the left and right eyes is Qa(,x)fl() and Qa(,x)fr() respectively.June 14, 2000Eric Dubois23Transmission of red and blue filtersJune 14, 2000Eric Dubois24Perceived Anaglyph Image with Glasses· The tristimulus values for the left and right views through the glasses are~ U lk (x ) =  Q( , x ) f l ( )pk ( ) d =  Vaj (x ) pk ( ) d j ( ) f l ( )dj =1 3 3=  alkjVaj (x ), k = 1,2,3j =1· orJune 14, 2000~ U l (x ) = A l Va (x )~ U r (x ) = A r Va (x ) Similarly,Eric Dubois 25Goal of Anaglyph reproductionWe want the anaglyph image to appear as similar as possible to the ideal stereoscopic image~  U l1 (x )  ~  U l 2 (x ) ~ U l 3 (x ) ~ U(x ) = RVa (x ) =  ~  U r1 (x ) ~ U r 2 (x ) ~  U r 3 (x ) Anaglyph 3DJune 14, 2000~  Vl1 (x )  ~  Vl 2 (x ) ~ Vl 3 (x ) ~ V (x ) =  ~  Vr1 (x ) ~ Vr 2 (x ) ~  Vr 3 (x ) Ideal 6DEric Dubois26Generation of Anaglyph Image· For each pixel location, we seek an element of the three-dimensional anaglyph subspace as close as possible to the original stereo image value which is in a six-dimensional space. · If we have a suitable distance metric, we can choose the value in the three-dimensional space that is closest to the original six-dimensional value. · This achieved by ProjectionJune 14, 2000Eric Dubois27Assumptions· The approximation is carried out independently at each sample location · The error metric at each point is a weighted ~ ~ squared error between U and V~ ~2 ~ ~ T ~ ~ U - V = (U - V ) W (U - V )· A global scaling of the Vaj is used to account for the attenuation of the filters.June 14, 2000Eric Dubois28Projection· Applying standard projection theory gives^ Va (x ) = R T WR( ) -1 T T = (R WR ) R WC 2 V (x )-1~ R WV (x )T· The 3 x 6 matrix (R WR ) R T WC 2 is fixed and can be precomputedT -1June 14, 2000Eric Dubois29Basketball ImageJune 14, 2000Eric Dubois30AnaglyphJune 14, 2000Eric Dubois31June 14, 2000Eric Dubois32June 14, 2000Eric Dubois33June 14, 2000Eric Dubois34June 14, 2000Eric Dubois35June 14, 2000Eric Dubois36Conclusion· A method to generate anaglyphs based on the mathematical description of the image display and perception process has been developed. · Some color reproduction is possible. · Better stereo rendition than conventional approaches.June 14, 2000Eric Dubois37What Else?· How to choose filters to give best results? · Can color rendition be improved? · Can the method be applied to time-shuttered stereo?June 14, 2000Eric Dubois38Thanks for coming!June 14, 2000Eric Dubois39`

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