1. Image Processing
고려대학교 컴퓨터 그래픽스 연구실
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2. Overview Image Representation Sampling and Reconstruction
What is an image?
Sampling and Reconstruction
Key steps in image processing
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3. A pixel is a sample, not a little square!!
What is an Image?
An image is a 2D rectilinear array of pixels
Continuous image
Digital image
A pixel is a sample, not a little square!!
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4. What is an Image? An image is a 2D rectilinear array of pixels
Continuous image
Digital image
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5. What is an Image? An image is a 2D rectilinear array of pixels
Continuous image
Digital image
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6. Image Acquisition Pixels are samples from continuous function
Photoreceptors in eye
CCD cells in digital camera
Rays in virtual camera
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7. Quantization Artifact due to limited intensity resolution
Frame buffers have limited number of bits per pixel
Physical devices have limited dynamic range
255
150 75
255
150 75
255
150 75
Blue channel
Green channel
Red channel
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8. Image Display Re-create continuous function from samples
Example: cathode ray tube
Image is reconstructed by displaying pixels with finite area (Gaussian)
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9. Image Resolution Intensity resolution Spatial 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
National Television System Committee
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10. Overview Image Representation Sampling and Reconstruction
What is an image?
Sampling and Reconstruction
Key steps in image processing
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11. Sampling and Reconstruction
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12. Sampling and Reconstruction
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13. Image Processing Pixel operations Filtering Warping Add luminance Blur
Add contrast
Filtering
Blur
Detect edge
Warping
Scale
Rotate
Warps
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14. Adjusting Brightness Simply scale pixel components
Must clamp to range (e.g., 0 to 255)
Original
Brighter
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15. Adjusting Contrast Compute mean luminance L for all pixels
Luminance = 0.30*r *g *b
Scale deviation from L for each pixel component
Must clamp to range (e.g. 0 to 255) L
Original
More contrast
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16. Image Processing Pixel operations Filtering Warping Add luminance Blur
Add contrast
Filtering
Blur
Detect edge
Warping
Scale
Rotate
Warps
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17. Adjusting Blurriness Convolve with a filter whose entries sum to one
Each pixel becomes a weighted average of its neighbors
Original
Blur
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18. Edge Detection
Convolve with a filter that finds differences between neighbor pixels
Original
Edge Detection
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19. Blurring and Convolution3
We call this “filter”
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20. Blurring and Convolution3
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21. Blurring and Convolution3
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22. Blurring and Convolution3
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23. Blurring and Convolution3
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24. Blurring and Convolution3
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25. Blurring and Convolution3
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26. Blurring and Convolution3
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27. Blurring and Convolution3
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28. Blurring and Convolution3
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29. Blurring and Convolution3
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30. Blurring and Convolution3
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31. Blurring and Convolution3
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32. Blurring and Convolution3
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33. Blurring and Convolution3
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34. Blurring and Convolution3
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35. Blurring and Convolution3
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36. Blurring and Convolution3
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37. Blurring and Convolution3
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38. Blurring and Convolution3
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39. Blurring and Convolution3
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40. Edge Detection
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41. Discretize Convolution
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42. Edge Detection Pixel alteration using convolution mask mask
int sumX, sumY, sum;
for( y=1 ; y<image_height-1 ; y++ )
for( x=1 ; x<image_width-1 ; x++ ) {
sumX=0;
for( j=0 ; j<3 ; j++ )
for( i=0 ; i<3 ; i++ ){
sumX += maskX[i][j]*image[x+i-1][y+j-1] }
sumY=0;
sumY += maskY[i][j]*image[x+i-1][y+j-1]
sum = abs(sumX)+abs(sumY);
if(sum > 255) sum =255;
if(sum < 0) sum = 0;
result_Image[x][y] = sum;
mask
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43. Edge Detection Various masks for edge detection Prewitt Sobel
Frei-Chen
Laplacian 1
Laplacian 2
Laplacian 3
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44. Image Processing Pixel operations Filtering Warping Add luminance Blur
Add contrast
Filtering
Blur
Detect edge
Warping
Scale
Rotate
Warps
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45. Image Warping Move pixels of image Mapping Resampling Warp
Source Image
Destination Image
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46. Overview Mapping Resampling Forward Reverse Point sampling
Triangle filter
Gaussian filter
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47. Mapping Define transformation
Describe the destination (x, y) for every location (u, v) in the source (or vice-versa, if invertible) v y u x
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48. Example Mappings Scale by factor : x = factor * u y = factor * v v y
0.8 u x
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49. Example Mappings Rotate by θ degrees: x = u cos θ – v sin θ
y = u sin θ + v cos θ x y v
Rotate 30 u
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50. Example Mappings Shear in X by factor : Shear in Y by factor :
x = u + factor * v
y = v
Shear in Y by factor :
x = u
y = v + factor * u u v x y
Shear X
1.3 u v x y
Shear Y
1.3
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51. Other Mappings Any function of u and v : x = fx(u, v) y = fy(u, v)
Fish-eye
Swirl
Rain
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52. Image Warping Implementation I
Forward mapping :
for(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); }
(u, v) f
(x, y)
Source Image
Destination Image
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53. Forwarding Mapping Iterate over source image y v Rotate -30 u x
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54. Forwarding Mapping – NOT
Iterate over source image
Many source pixels can map to same destination pixel x y u v
Rotate
-30
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55. Forwarding Mapping – NOT
Iterate over source image
Some destination pixels may not be covered
Many source pixels can map to same destination pixel x y u v
Rotate
-30
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56. Image Warping Implementation II
Reverse mapping
for(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); }
(u, v) f
(x, y)
Source Image
Destination Image
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57. Reverse Mapping Iterate over destination image
At least, no pixel in destination goes empty
Must resample source
May oversample, but much simpler x y u v
Rotate
-30
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58. Usually (u, v) is not an integer
Resampling
Evaluate source image at arbitrary (u, v)
Usually (u, v) is not an integer
(u, v)
(x, y)
Source Image
Destination Image
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59. Overview Mapping Resampling Forward Reverse Point sampling
Triangle filter
Gaussian filter
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60. This method is simple, but it causes aliasing
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 causes aliasing x y u v F
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61. Triangle Filtering Convolve with triangle filter Input Output
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62. Triangle Filtering 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(x, y) = linear interpolation of “a” and “b” a
(u1, v2)
(u2, v2)
(u, v)
(u1, v1)
(u2, v1) b
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63. Width of Gaussian kernel affects bluriness
Gaussian Filtering
Convolve with Gaussian filter
Input
Output
Width of Gaussian kernel affects bluriness
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64. Gaussian Filtering Compute weighted sum of pixel neighborhood :
Weights are normalized values of Gaussian function r
(u, v)
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65. Filtering Methods Comparison
Trade-offs
Aliasing versus blurring
Computation speed
Point
Bilinear
Gaussian
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66. Image Warping Implementation III
Reverse mapping
for(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); }
(u, v) f
(x, y)
Source Image
Destination Image
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67. Image Warping Implementation III
Reverse mapping
for(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); }
(u, v) f
(x, y) w
Source Image
Destination Image
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68. Example: Scale Scale (src, dst, sx, sy) : float w ≈ max(1/sx, 1/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); } v y
(u, v)
Scale
0.5
(x, y) u x
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69. Example: Rotate Rotate (src, dst, theta)
for(int x=0; x<xmax; x++) {
for(int y=0; y<ymax; y++) {
float u = x*cos(-θ)-y*sin(-θ)
float v = x*sin(-θ)+y*cos(-θ)
dst(x,y) = resample_src(u,v,w); } x y v
(u, v)
(x, y)
Rotate 30 u
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70. 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)*θ)
float v = rot(dist(y,ycenter)*θ)
dst(x,y) = resample_src(u,v,w); } v
(u, v) y
(x, y)
Swirl 45 u x
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