image 2012, fall. image processing quantization uniform quantization halftoning & dithering...
TRANSCRIPT
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Image
2012, Fall
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Image Processing
Quantization Uniform Quantization Halftoning & Dithering
Pixel Operation Add random noise Add luminance Add contrast Add saturation
Filtering Blur Detected edges
Warping Scale Rotate Warp
Combining Composite Morph
Ref] Thomas Funkhouser, Princeton Univ.
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What is an Image?
An image is a 2D rectilinear array of samples
A pixel is a sample, not a little square
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Image Resolution
Intensity resolution Each pixel has only “Depth” bits for colors/intensities
Spatial resolution Image has only “Width” x “Height” pixels
Temporal resolution Monitor refreshes images at only “Rate” Hz
Width x Height Depth Rate
NTSC 640x480 8 30
Workstation 1280x1024 24 75
Film 3000 x 2000 12 24
Laser Printer 6600x5100 1 -
Typical Resolutions
Hei
ght
WidthDepth
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Source of Error
Intensity quantization Not enough intensity resolution
Spatial aliasing Not enough spatial resolution
Temporal aliasing Not enough temporal resolution
),(
22 )),(),((yx
yxPyxIEReal value Sample value
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Quantization
Artifact due to limited intensity resolution Frame buffers have limited number of bits per pixel Physical devices have limited dynamic range
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Uniform Quantization
)5.0),((),( yxItruncyxP
반올림 (Round)
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Uniform Quantization
Image with decreasing bits per pixel
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Reducing Effects of Quantization
Our eyes tend to integrate or average the fine detail into an overall intensity
Halftoning A technique used in newspaper printing The process of converting a continuous tone image into an
image that can be printed with one color ink (grayscale) or four color inks (color)
Dithering Dithering is used to create a wide variety of patterns for use
as backgrounds, fills and shadings, as well as for creating halftones, and for correcting aliasing.
Halftones are created through a process called dithering Dithering Methods( 방법론 ) , Halfton result( 결과물 )
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Classical Halftoning
Use dots of varying size to represent intensities Area of dots proportional to intensity in image
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Halftoning
A technique used in newspaper printing Only two intensities are possible, blob of ink and no
blob of ink
But, the size of the blob can be varied Also, the dither patterns of small dots can be used
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Classical Halftoning
Original Image Halfton Image
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Halfton patterns
Use cluster of pixels to represent intensity Trade spatial resolution for intensity resolution
2 by 2 pixel grid patterns
3 by 3 pixel grid patterns
mask
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Halfton patterns
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Dithering
Distribute errors among pixels Exploit spatial integration in our eye Display greater range of perceptible intensities
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Halftoning – Moire Patterns
Moire[more-ray] patterns Repeated use of same dot pattern for particular shade results
in repeated pattern (Perceived as a moire pattern) result from overlapping repetitive elements Instead, randomize halftone pattern
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Halftoning – Moire Patterns
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Signal Processing (1/2)
Signal Real World : Continuous Signal Digital World: Discrete Signal
Image spatial domain
• not temporal domain
• intensity variation
over space
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Signal Processing (2/2)
Sampling and reconstruction process Sampling
• The process of selecting a finite set of values from a signal
• Samples (the selected values)
Reconstruction• recreate the original continuous signal from the samples
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Sampling and Reconstruction
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Aliasing
In general Artifact due to under-sampling or poor reconstruction
Specifically, in graphics Spatial aliasing Temporal aliasing
Sampling below the Nyquist rate
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Nyquist rate and aliasing
Nyquist rate lower bound on the sampling rate Sampling at the Nyquist rate
• sampling rate > 2* max frequency
주파수 (frequency): 초당 사이클의 횟수 (Hz)
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Spatial Aliasing
Artifact due to limited spatial resolution
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Spatial Aliasing
Artifact due to limited spatial resolution
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Temporal Aliasing
Artifact due to limited temporal resolution Spinning Backward
• The wheel is spinning at 5 revolution per second– 3rd row appear to be spinning backward at revolution per
second
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Temporal Aliasing
Artifact due to limited temporal resolution Flickering
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Anti-Aliasing
Sample at higher rate Not always possible Doesn’t always solve problem
Pre-filter to form bandlimited signal Form bandlimited function(low-pass filter) Trades aliasing for blurring
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Pixel Operations
Grayscale Compute luminance L L=0.30R+0.59G+0.11B (old)
0.2125R+0.7154G+0.0721B (CRT, HDTV)
Original Image Grayscale Image
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Pixel Operations
Negative Image Simply inverse pixel components Ex) RGB(5, 157, 178) RGB(250, 98, 77)
Original Image Negative Image
(R, G, B) (255-R, 255-G, 255-B)
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Pixel Operations
Adjusting Brightness Simply scale pixel components
• Must clamp to range (e.g., 0 to 255)
(R, G, B) (R, G , B) * scale
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Pixel Operations
Adjusting Contrast Compute mean luminance L for all pixels
• Luminance = 0.30* r + 0.59*g + 0.11*b
Scale deviation from L for each pixel component• Must clamp to range (e.g., 0 to 255)
R L + (R-L)*scaleG L + (G-L)*scaleB L + (B-L)*scale
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Pixel Operations
Changing Brightness
Changing Contrast
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Pixel Operations
Adjusting Saturation Color Convert RGB HSV Scale from S for each pixel component Color Convert HSV RGB
• Must clamp to range (e.g., 0 to 255)
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Filtering
Convolution Spatial domain
• Output pixel is weighted sum of pixels in neighborhood of input image
• Patten of weights is the “filter”
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Filtering
Convolution
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Filtering
Adjust Blurriness Convolve with a filter whose entries sum to one
• Each pixel becomes a weighted average of its neighbors
Filter Sum = 1
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Filtering
Edge Detection Convolve with a filter that finds differences between
neighbor pixels
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Filtering
Sharpening Convolve with a Sharpening filter
010
151
010
Filter
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Filtering
Embossing Convert the image into grayscale Convolve with a Embossing filter Plus 0.5 for each pixel
• Must clamp to range (e.g., 0 to 255)
100
010
002
Filter
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Summary
Image representation A pixel is a sample, not a little square Images have limited resolution
Halftoning and dithering Reduce visual artifacts due to quantization Distribute errors among pixels
• Exploit spatial integration in our eye
Sampling and reconstruction Reduce visual artifacts due to aliasing Filter to avoid undersampling
• Blurring is better than aliasing
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Image Processing
Quantization Uniform Quantization Halftoning & Dithering
Pixel Operation Add random noise Add luminance Add contrast Add saturation
Filtering Blur Detected edges
Warping Scale Rotate Warp
Combining Composite Morph
Ref] Thomas Funkhouser, Princeton Univ.
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Image Warping
Move pixels of image Mapping
• Forward
• Reverse
Resampling• Point sampling
• Triangle Filter
• Gaussian filter
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Mapping
Define transformation Describe the destination (x,y) for every location (u,v) in the
source (or vice-verse, if invertible)
Source (u, v) Destination (x, y)
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Example Mappings
Scale by factor x = factor * u y = factor * v
Source (u, v) Destination (x, y)
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Example Mappings
Rotate by degrees x = ucosvsin y = usinvcos
Source (u, v) Destination (x, y)
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Example Mappings
Shear in X by factor x = u + factor * v y = v
Shear in Y by factor x = u y = v + factor * u
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Other Mappings
Any function of u and v X = fx (u, v)
Y = fy (u, v)
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Image Warping Implementation I
Forward mappingfor (int u =0; u < umax; u++) {
for (int v = 0; v < vmax; v++) {
float x = fx (u, v);
float y = fy (u, v);
dst (x, y) = src(u, v) ;
}
}
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Forward Mapping
Iterate over source image Many source pixels can map to same destination pixel Some destination pixels may not be covered
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Image Warping Implementation II
Reverse mappingfor (int x =0; x < xmax; x++) {
for (int y = 0; y < ymax; y++) {
float u = fx-1 (x, y);
float v = fy-1 (x, y);
dst (x, y) = src(u, v);
}
}
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Reverse Mapping
Iterate over destination image Must resample source May oversample, but much simpler
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Resampling
Evaluate source image at arbitrary (u,v) (u, v) does not usually have integer coordinates
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Resampling
Resampling Point sampling Triangle filter Gaussain filter
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Point Sampling
Take value at closest pixel int iu = trunc(u + 0.5) int iv = trunc(v + 0.5) dst(x, y) = src(iu, iv)
This method is simple, but it cause aliasing
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Filtering
Compute weighted sum of pixel neighborhood Weights are normalized values of kernel function Equivalent to convolution at samples
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Triangle Filtering
Kernel is triangle function
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Triangle Filtering (with width = 1)
Bilinearly interpolate four closest pixels a = linear interpolation of src(u1, v2) and src(u2, v2) b = linear interpolation of src(u1, v1) and src(u2, v1) dst = linear interpolation of “a” and “b”
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Gaussian Filtering
Kernel is Gaussian function
Filter width =2
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Filtering Methods Comparison
Trade-offs Aliasing versus blurring Computation speed
Point Bilinear Gaussian
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Image Warping Implementation
Reverse mappingfor (int x =0; x < xmax; x++) {
for (int y = 0; y < ymax; y++) {
float u = fx-1 (x, y);
float v = fy-1 (x, y);
dst (x, y) = resample_src(u, v, w);
}
}
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Example: Scale
scale (src, dst, sx, sy) :Float w = max (1.0/sx, 1.0/sy)
for (int x =0; x < xmax; x++) {
for (int y = 0; y < ymax; y++) {
float u = x / sx;
float v = y / sy;
dst (x, y) = resample_src(u, v, w);
}
}
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Example: Rotate
Rotate (src, dst, theta) :for (int x =0; x < xmax; x++) {
for (int y = 0; y < ymax; y++) {
float u = x*cos(-theta)y*sin(-theta);
float v = x*sin(-theta)y*cos(-theta);
dst (x, y) = resample_src(u, v, w);
}
}
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Example: Fun
Swirl (src, dst, theta) :for (int x =0; x < xmax; x++) {
for (int y = 0; y < ymax; y++) {
float u = rot(dist(x, xcenter)*theta);
float v = rot(dist(y, yecnter)*theta);
dst (x, y) = resample_src(u, v, w);
}
}
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Combining images
Image compositing Blue-screen mattes Alpha channel
Image morphing Specifying correspondence Warping Blending
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Image Compositing
Separate an image into “elements” Render independently Composite together
Application Cel animation Chroma-keying Blue-screen matting
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Blue Screen Matting
Composite foreground and background images Create background image Create foreground image with blue background Insert non-blue foreground pixels into background
Problem : no partial coverage
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Alpha Channel
Encodes pixel coverage informations = 0 no coverage (or transparent) = 1 full coverage (or opaque) 0 < < 1 partial coverage (or semi-transparent)
Example: = 0.3
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Composite with Alpha
Composite with Alpha Control the linear interpolation of foreground and
background pixels when elements are composited
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Pixels with Alpha
Alpha channel convention (r, g, b, a) represents a pixel that is a covered by
the color C = (r/a, g/a, b/a)• Color components are premultiplied by a
• Can display (r, g, b) value directly
• Closure in composition algebra
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Semi-Transparent Objects
Suppose we put A over B background G
How much of B is blocked by A ? A
How much of B show through A ?A)
How much of G shows through both A and B ?A) B)
αAA+ (1-αA )αBB+ (1-αA )(1-αB )G = A over[B over G]
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Opaque Objects
How do we combine 2 partially covered pixels? 3 possible colors (0, A, B) 4 regions (0, A, B, AB)
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Composition Algebra
12 reasonable combinations
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Image Morphing
Animate transition between two images
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Cross-Dissolving
Blend images with “over” operator alpha of bottom image is 1.0 alpha of top image varies from 0.0 to 1.0
blend(i, j) = (1-t) src(i, j) + t dst(i, j) (0 <= t <= 1)
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Image Morphing
Combines warping and cross-disolving
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Feature Based Morphing
Beier & Neeley use pairs of lines to specify warp Given p in dst image, where is p’ in source image ?
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Feature Based Morphing
Feature Matching
Image Warping Image Warping
Morphed Image
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Feature Based Morphing
Morphing
Warping Warping
Black Or White-Michael Jackson
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Image Processing
Quantization Uniform Quantization Halftoning & Dithering
Pixel Operation Add random noise Add luminance Add contrast Add saturation
Filtering Blur Detected edges
Warping Scale Rotate Warp
Combining Composite Morph
Ref] Thomas Funkhouser, Princeton Univ.