Last TimeTodayDynamic RangeTone ReproductionDifferent GoalsAn Artist’s ApproachMore VermeerMeasurementsLuminous EfficiencyColor and LuminanceCIE (Y,x,y)Automatic Tone ReproductionLinear MappingsNon-Linear MappingsHistogram Methods (Ward Larson, Rushmeier and Piatko, TVCG 97)Building HistogramsCumulative DistributionHistogram EqualizationNaïve HistogramAvoiding Super-SensitivityBetter Histogram AdjustmentCumulative DistributionsMore Histogram MethodsLocal MethodsBasic IdeaWhat’s the Problem?For ComparisonLCIS ProblemsLocal Tone ReproductionEdge Preserving Filters (Durand and Dorsey, SIGGRAPH 2002)Robust EstimationResultsThe NPR AssignmentA. Choosing a PaperB. Read the PaperC. Prepare a TalkD. Give your TalkGradingClass ProjectsSuitable Projects03/2/05 © 2005 University of WisconsinLast Time•Sub-surface and Atmospheric Scattering03/2/05 © 2005 University of WisconsinToday•Tone-Reproduction: Part 1•The NPR presentation assignment•Projects03/2/05 © 2005 University of WisconsinDynamic Range•Real scenes contain both very bright and very dark regions•Dynamic range is the ratio of the brightest to darkest points in the scene•Standard measurement is candelas per m2 (defined shortly)•For example, in the interior of the church the dynamic range is 100,000 to 103/2/05 © 2005 University of WisconsinTone Reproduction•The human eye can globally adapt to about 109:1–Adjusts for the average brightness we perceive in one scene–Global adaptation lets us see in very low light or very bright conditions–But it’s slow - how slow?•The human eye can locally adapt to about 10,000:1–In a single scene (global adaptation level), we can perceive contrast across this range•Most display devices have a very limited dynamic range–On the order of 100:1 for a very good monitor or film•Tone reproduction is the problem of making the 10,000:1 scene look right on a 100:1 display device03/2/05 © 2005 University of WisconsinDifferent Goals•Option 1: Reveal as much detail as possible in the image given the limited dynamic range–For conveying information, but not necessarily realism•Option 2: Reveal what would be available if the viewer would really be there–Perceptual limits place limits on what we can see under a given set of viewing conditions03/2/05 © 2005 University of WisconsinAn Artist’s Approach•Artists have known how to do this for centuries•e.g. Vermeer (spot the tricks)03/2/05 © 2005 University of WisconsinMore Vermeer03/2/05 © 2005 University of WisconsinMeasurements•We have discussed things in terms of radiometry, with quantities such as Watts, meters, seconds, steradians•Photometry deals with radiometric quantities pushed through a response function–A sensor (the human eye) has a response curve, V–Luminance (candelas per meter squared, cd/m2) is the integral of radiance against the luminous efficiency function (the sensor response function)03/2/05 © 2005 University of WisconsinLuminous EfficiencydRV )()( Luminance03/2/05 © 2005 University of WisconsinColor and Luminance•The CIE XYZ color space is intended to encode luminance in the Y channel•To get from RGB to XYZ, apply the following linear transform:–Taken from Sillion and Puech, other sources differbgrZYX78.008.000.008.071.033.014.021.067.0ZYXbgr284.1169.0083.0023.0652.1814.0261.0482.0730.103/2/05 © 2005 University of WisconsinCIE (Y,x,y)•The XYZ space includes brightness info with color info–X and Z get bigger as the color gets brighter•To avoid this, use (Y,x,y)–x=X/(X+Y+Z)–y=Y/(X+Y+Z)•(x,y) are chromaticity values03/2/05 © 2005 University of WisconsinAutomatic Tone Reproduction•There are three main classes of solutions:–Global operators find a mapping from image to display luminance that is the same for every pixel–Local operators change the mapping from one pixel to the next–Perceptually guided operators use elements of human perception to guide the tone reproduction process03/2/05 © 2005 University of WisconsinLinear Mappings•The simplest thing to do is to linearly map the highest intensity in the image to the highest display intensity, or the lowest to the lowest–This gives very bad results, shown for mapping the maps lowest to lowest03/2/05 © 2005 University of WisconsinNon-Linear Mappings•Instead of linear, define some other mapping: Ld=M(Lw)–Display luminance is some function of the world luminance•It is important to retain relative brightness, but not absolute brightness–If one point is brighter than another in the source, it should be brighter in the output–The mapping M should be strictly increasing03/2/05 © 2005 University of WisconsinHistogram Methods(Ward Larson, Rushmeier and Piatko, TVCG 97)•In any one scene, the dynamic range is not filled uniformly•The aim of histogram methods is to generate a mapping that “fills in the gaps” in the range03/2/05 © 2005 University of WisconsinBuilding Histograms•Work in brightness: B=log10(L)–Humans are more sensitive to “brightness,” but the formula is a hack•The histogram is a count of how many pixels have each brightness–Choose a set of bins–Break the image into chunks that subtend about 1 of arc•Assumes you know the camera–Average brightness in each chunk–Count chunks that fall in each bin, f(bi)–Result is graph on previous image03/2/05 © 2005 University of WisconsinCumulative Distribution•We can consider the histogram counts as the probability of seeing a pixel in each range•The cumulative distribution function is defined:   iibibbibfTTbfbP03/2/05 © 2005 University of WisconsinHistogram Equalization•The aim is an output histogram in which all the bins are roughly equally filled•The naïve way to do this is to set:•Then, go through and convert brightness back into luminance for display       wdmindmaxdmindeBPLLLB logloglog 03/2/05 © 2005 University of WisconsinNaïve HistogramLinear left.Histogram right.What went wrong?03/2/05 © 2005 University of WisconsinAvoiding Super-Sensitivity•We should make sure that we do not increase contrast beyond the linear mapping contrast:•This imposes a constraint on the frequency in each bin:•Reduce the count of