Dec 16 2013 Visualization with 3 D CG

Dec. 16, 2013 Visualization with 3 D CG Digital 2 D Image Basic Masaki Hayashi

2 D Image Digitization

2 D coordinate in image processing

Scanning

Gray scale & RGB pixel Grey scale (Black & white) RGB (Color)

Image size Spatial pixel n Size (Resolution) 320 x 240 640 x 480 SDTV 1920 x 1080 HDTV 3840 x 2160 4 K 4096 x 2160 4 K (cinema) 7680 x 4320 8 K. . . V size H size

Image depth pixel n Depth (sampling bit rate) 8 bits (256 levels) 10 bits (1024 levels) 12 bits (4096 levels) 16 bits, . . . V size n Depth and Color Depth H size 24 bits RGB || 8 bits X 3 || 256 X 256 = 1. 677 million colors

Frame rate Temporal ■Frame frequency (FPS) 24 p 25 p 30 p 50 i 60 i 50 p 60 p 120 p. . . . t i: Interlace p: progressive Temporal (time) resolution => Frame frequency (Hz) => Frame rate => FPS (Frame per second)

Aspect ratio 512 1: 1 3456 512 640 3: 2 4: 3 (TV in the past) 480 (Film) 2304 1920 16 : 9 Square pixel, basically (HDTV, 4 K, 8 K) 1080

Features of image (summary) n Resolution Sharpness, spatial detail n Depth Dynamic range n Frame rate Smoothness of moving object

Resolution family in video 8 K (Super Hi-Vision) 7680 X 4320 16 : 9 4 K (QFHD) Quad-Full-HD 3840 X 2160 16 : 9 2 K (HDTV) 1920 X 1080 SD 16 : 9 720 X 480 ü Television: 4 K (QFHD): 3840 X 2160, 16: 9 ü Digital cinema: 4 K: 4096 X 2160, 17: 9(approx. ) 256: 135

Pixel density ppi (pixel per inch) (dpi: dot per inch, is for printer) Retina display (i. Pad Retina) 9. 7 inch, 2048 x 1536 264 ppi 4 K display 56 inch, 3840 x 2160 79 ppi even a 8 K is not enough. . .

Viewing distance Standard viewing distance ~ = 3 H (HDTV) 1. 5 H (4 K) H 3 H (immersive sensation, presence, etc. point of view) 56 inch monitor => 70 cm Virtical

Image compression

Image format JPEG l Most popular l Mosquito noise, Blocky noise l Not suitable for Logo, text, cartoon… GIF l Popular in the past. Motion-GIF l Only 256 colors PNG l Improved version of GIF, Most used on the Internet l Un-limited color. OK for both natural image and logo stuff BMP l Bitmap. Uncompressed, Microsoft

How JPEG compress image INPUT Image 8× 8 spatial 8× 8 frequencyl Important Split into 8× 8 blocks ü Approx. 1/10 compress ü 8× 8 blocky noise ü Mosquito noise at sharp edge Less important Discrete Cosine Transform (DCT) Quantization & Entropy coding JPEG data series OUTPUT

How GIF compress image INPUT 16777216 colors 256 colors Reduce colors LZW compress ü Good for logo, font, cartoon Bad for photograph ü No blocky noise, no mosquito ü Taken over by PNG GIF data series OUTPUT

Image processing

Image and array RGB Luminance and Chroma Luminance Y = 0. 3 R + 0. 59 G + 0. 11 B Chroma (Hue and Saturation) CR = R - Y CB = B - Y

Color scheme Chroma Hue and Saturation H = tan-1 (CR/CB) CR S = CR 2 + CB 2 S H CB

Color scheme R (Red) H (Hue) G (Green) S (Saturation) B (Blue) B (Brightness) Graphics: Copyright © Department of Computer Engineering and Computer Science, California State University, Long Beach

Color bar White Yellow Cyan Magenta Green Blue Red

Lookup table (LUT) Output pixel value 256 0 256 Input pixel value out[0][i][j] = LUT[ in[0][i][j] ] ; LUT[ 0 ] = 0; LUT[ 1 ] = 1; LUT[ 2 ] = 2; LUT[ 3 ] = 3; LUT[ 4 ] = 4; LUT[ 5 ] = 5; LUT[ 6 ] = 6; LUT[ 7 ] = 7; ……. LUT[ 255 ] = 255;

Lookup table (LUT) LUT Posterization Input image LUT Binarization Copyright © CG-Arts

Histogram Input image Histogram Intensity distribution of an image

Histogram Correction

Spatial filtering -1 -1 9 -1 -1 Filter (3 x 3 kernel) 50 50 50 x(-1) + 150 x(-1) + 100 x 9 + 100 x(-1) + 120 x(-1) = 90 convolution 150 100 100 90 120 120 Input image Output image

Smoothing 1/9 1/9 1/9 Mean filter

Smoothing 120 122 140 100 110 145 90 120 135 Input image 145 140 135 122 120 110 100 90 Sorting by numerical order Median filter 120 Output image

Smoothing σ=1. 0 Gaussian smoothing Text: © 2004 Robert Fisher, Simon Perkins, Ashley Walker, Erik Wolfart

Edge detection 0 1 1 1 -1 2 -1 1 -4 1 1 -8 1 2 -4 2 0 1 1 1 -1 2 -1 Laplacian filter Second spatial derivative of an image

Edge detection 1. 0 0. 0 1 -2 1 0. 0 -1. 0

Edge detection Laplacian is much noise sensitive in Gaussian Smoothing Laplacian To reduce high frequency noise in the output image out

Edge enhancement using edge signal detected by laplacian + in out + - Laplacian 2. 0 1 -2 1 1. 0 0. 0 -1 Often refered as “- Laplacian” 0 4 -1 0

Unsharp filter (edge enhancement) + in + Smoothing out + + + - x k k : scaling constant for adjusting enhancement Text: © 2004 Robert Fisher, Simon Perkins, Ashley Walker, Erik Wolfart

Spatial domain vs Frequency domain Spatial signal transforming re-transforming Frequency signal f f

Spatial domain vs Frequency domain Original image Frequency signal DFT IDFT Spatial domain Frequency domain DFT: Discrete Fourier Transform

Digital filter DFT Original image Frequency signal apply Mask = remove high frequency Filtered signal Output image IDFT Spatial domain Frequency domain

Image magnification Input 2 times magnification Output Gap If output pixel position is calculated by using input pixel position

Image magnification No interpolation (Nearest neighbor) Original image With interpolation (Bi-linear) 5 times zooming

Image shrinking 1/2 shrinking Input This works but not enough Output Aliasing problem

Image shrinking Input Output 5 times shrinking Undesired signal called "aliasing" appears

Sub-sampling & unti-aliasing Aliasing fp / 4 fp / 2 fp / 4 LPF No aliasing fp / 2 fp / 4

Unti-aliasing No untialiasing With unti-aliasing (Low pass filtered prior to the shrinking)

Image magnification Input 2 times magnification Output Input pixel position should be calculated by output pixel position Interpolated from the neighbored 4 pixel values