Point OperationsOverviewVisual Angle and Spatial FrequencyOverall Monochrome Vision ModelImage Fidelity CriteriaMean-square CriterionImage Enhancement via Point OperationsPoint Operations / Intensity TransformTypical Types of Gray-level TransformationExample: Negative TransformationExample: Log TransformationGamma Characteristics & Gamma CorrectionExample of Gamma CorrectionLuminance HistogramLuminance Histogram (cont’d)Example: Balanced and Unbalanced HistogramsContrast Stretching for Low-Contrast ImagesContrast Stretching: ExampleClipping and ThresholdingExamples of Histogram EqualizationEqualization Example (cont’d)How to Do Histogram Equalization?The Math Behind Histogram EqualizationHistogram Equalization AlgorithmHistogram Equalization: A Mini-ExampleSummary: Contrast Stretching vs. Histogram Eq.Generalization of Histogram EqualizationVisual QuantizationUse Dithering to Remove Contour ArtifactsSummary of Today’s LectureSlide 38BackupExampleTool-1: Contrast QuantizationTool-2: “Pseudorandom Noise” QuantizationHalftoneDithering for Halftone ImagesExamples of Halftone ImagesM. Wu: ENEE631 Digital Image Processing (Spring'09)Point OperationsPoint OperationsSpring ’09 Instructor: Min Wu Electrical and Computer Engineering Department, University of Maryland, College Park bb.eng.umd.edu (Select ENEE631 S’09) [email protected] Spring’09ENEE631 Spring’09Lecture 3 (2/2/2009)Lecture 3 (2/2/2009)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [2]OverviewOverviewLast Time–Color representation and perceptionnot a precise spectrum analyzer => perceive color via 3 types of cones–Human visual properties for monochrome visionnot a precise intensity/energy meter => depend on surrounding contrast and spatial frequencyToday–Wrap up monochrome vision: spatial frequency and quality metrics–Point processing (zero-memory operations)See reading list on the last slide of each lecture notesAssignment-1 will be posted on course webpageUMCP ENEE631 Slides (created by M.Wu © 2004; 2009)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [3]dotdotVisual Angle and Spatial FrequencyVisual Angle and Spatial FrequencyVisual angle matters more than absolute size and distance–Smaller but closer object vs. larger but farther object–Eyes can distinguish about 25-30 lines per degree in bright illumination25 lines per degree translate to 500 lines for distance=4 x screenheightSpatial Frequency–Measures the extent of spatial transitionin unit of “cycles per visual degree”Visibility thresholds–Eyes are most sensitive to medium spatial freq. and least sensitive to high frequencies ~ similar to a band-pass filter–More sensitive to horizontal and vertical changes than other orientationsUMCP ENEE408G Slides (created by M.Wu & R.Liu © 2002)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [5]Overall Monochrome Vision ModelOverall Monochrome Vision ModelFrom Jain’s Fig.3.9 (pp57)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [6]Image Fidelity CriteriaImage Fidelity CriteriaSubjective measures–Examination by human viewers–Goodness scale: excellent, good, fair, poor, unsatisfactory–Impairment scale: unnoticeable, just noticeable, … –Comparative measures with another image or among a group of imagesObjective (Quantitative) measures–Mean square error and variations–Pro:Simple, less dependent on human subjects, and easy to handle mathematically–Con:Not always reflect human perceptionUMCP ENEE631 Slides (created by M.Wu © 2001)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [7]Mean-square CriterionMean-square CriterionAverage (or sum) of squared difference of pixel luminance between two imagesSignal-to-noise ratio (SNR)– SNR = 10 log10 ( s2 / e2 ) in unit of decibel (dB)s2 image variancee2 variance of noise or error– PSNR = 10 log10 ( A2 / e2 )  A is peak-to-peak value PSNR is about 12-15 dB higher than SNRUMCP ENEE631 Slides (created by M.Wu © 2001)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [8]Image Enhancement via Point OperationsImage Enhancement via Point OperationsUMCP ENEE631 Slides (created by M.Wu © 2004)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [9]Point Operations / Intensity TransformPoint Operations / Intensity TransformBasic idea–“Zero memory” operationeach output of a pixel only depend on the input intensity at the pixel–Map a given gray or color level u to a new level v, i.e. v = f ( u )–Doesn’t bring in new info.–But can improve visual appearance or make features easier to detectExample-1: Color coordinate transformations– RGB of each pixel  luminance + chrominance components  etc.Example-2: Scalar quantization– quantize pixel luminance/color with fewer bitsinput gray level uoutput gray levelvUMCP ENEE631 Slides (created by M.Wu © 2001/2004)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [10]UMCP ENEE631 Slides (created by M.Wu © 2004)Typical Types of Gray-level TransformationTypical Types of Gray-level TransformationFigure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)LM. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [11]Example: Negative TransformationExample: Negative TransformationUMCP ENEE631 Slides (created by M.Wu © 2004)Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)M. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [12]Example: Log TransformationExample: Log TransformationUMCP ENEE631 Slides (created by M.Wu © 2004)Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)LU~ logLM. Wu: ENEE631 Digital Image Processing (Spring'09) Lec3 – Point Operations [14]Gamma Characteristics & Gamma CorrectionGamma Characteristics & Gamma CorrectionNon-linearity in CRT display–Voltage U vs. Displayed luminance L’ L’ ~ U  where  = 2.0 ~ 2.5Use preprocessing to compensate -distortion–U ~ L 1/  –log(L) gives similar compensation curve to -correction => used for many practical applications–Camera may have L1/c capturing distortion with c = 1.0-1.7 Power-law transformations are also useful for