This document discusses different methods for applying blur filters to images, including box blur, Gaussian blur, and optimizations. It compares the performance of naive box blur, optimized box blur, and using the vImage and Core Image frameworks. Core Image Gaussian blur is fastest, taking around 0.1 seconds for radii up to 1000, while naive box blur takes over 5000 seconds for radius 10 due to its quadratic runtime complexity. The document provides code samples and explanations of box blur, Gaussian blur, and how to implement them efficiently.

1. BLUR FILTER
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2. HANPO
SBACE - Director of Visual & Interface Design
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3. Why?

5. i.Frame Exhibition

6. Instagram Cam Path

7. Instagram

8. Path

9. Cam

10. What?

12. How?

13. Image Data

14. Pixel
Image (2D array of pixels)
RGB 115,41,41 RGB 98,49,49 RGB 212,168,32
RGB 115,41,41 RGB 98,49,49 RGB 255,243,182
RGB 115,41,41 RGB 98,49,49 RGB 255,251,236

15. Naïve Box Blur
Box blur - 3*3 Matrix of 1/9 * determinant matrix
1 1 1
1 1 1
1 1 1

16. Naïve Box Blur
RGB 115,41,41 RGB 98,49,49 RGB 212,168,32
RGB 115,41,41 RGB 98,49,49 RGB 255,243,182
RGB 115,41,41 RGB 98,49,49 RGB 255,251,236
RGB 151,104,80

17. Naïve Box Blur
Image convolution - the convolution of a 2D image is O(m2*n2)
For it to be fast you must implement it as an accumulator, not a convolution loop.
for each row
for each col
set count to 0
for every neighboring pixel within the radius m in the x direction
for every neighboring pixel within the radius m in the y direction
add the color to the total
count++
final_color = total/count
setpixel(current x, current y, final_color)

18. Calculate all Pixels
Sample image 4 x 3 pixels, radius is 1

19. Box Blur R:0 R:1 R:3
R:6 R:10 R:20

20. Edge Handling

21. Better Box Blur
Image convolution - the convolution of a 2D image is O(n^2 * 2m)
For it to be fast you must implement it as an accumulator, not a convolution loop.
for each row
for every neighboring pixel within the radius m in the x direction
add the color to the total
count++
final_color = total/count
setpixel(current x, current y, final_color)
!
repeat above for the columns

22. Calculate all Pixels
Sample image 6 x 6 pixels, radius is 2
in the x direction
in the y direction
if x <= r
for var _i=i-x; _i<=i+r; _i++
if x > r && x < (w-r)
for var _i=i-r; _i<=i+r; _i++
if x >= (w-r)
for var _i=i-r; _i<=i+(w-x); _i++
if _y <= r
for var _i=0; _i<=_y+r; _i++
let currentIndex = _i*w+_x
if r < _y && _y < (h-r)
for var _i=_y-r; _i<=_y+r; _i++
let currentIndex = _i*w+_x
if _y >= (h-r)
for var _i=_y-r; _i<=(h-1); _i++
let currentIndex = _i*w+_x

23. R:0 R:1 R:3
R:6 R:10 R:20
Better Box Blur

24. Compare
Box Blur & Better Box Blur
Size: 512 x 512 Device: iPad mini 2
Box Blur Better Box Blur
Radius:1 112.4061s 7.1371s
Radius:2 300.8143s 7.1586s
Radius:3 586.2660s 7.2406s
Radius:6 1958.8380s 7.3746s
Radius:10 5017.5250s 7.6009s
Radius:20 8.1089s

25. Convolution
for each image row in output image:
for each pixel in image row:
!
set accumulator to zero
!
for each kernel row in kernel:
for each element in kernel row:
!
if element position corresponding* to pixel position then
multiply element value corresponding* to pixel value
add result to accumulator
endif
!
set output image pixel to accumulator

26. Accelerate Framework
Consists of two frameworks: vImage and vecLib
Available in OS X v10.4
Use vector co-processor (CPU-based)
Designed to run various mathematical operations with data
Well optimized and uses SIMD

27. vImage
Accelerate Framework
func vImageBoxConvolve_ARGB8888(_ src: UnsafePointer<vImage_Buffer>,
_ dest: UnsafePointer<vImage_Buffer>,
_ tempBuffer: UnsafeMutablePointer<Void>,
_ srcOffsetToROI_X: vImagePixelCount,
_ srcOffsetToROI_Y: vImagePixelCount,
_ kernel_height: UInt32,
_ kernel_width: UInt32,
_ backgroundColor: UnsafeMutablePointer<UInt8>,
_ flags: vImage_Flags) -> vImage_Error

28. vImage Blur R:0 R:1 R:3
R:6 R:10 R:20

29. Compare
Box Blur Better Box Blur vImage
Radius:1 112.4061s 7.1371s first: 0.0292s
second: 0.0065s
Radius:2 300.8143s 7.1586s first:0.0260
second:0.0063
Radius:3 586.2660s 7.2406s first: 0.0410s
second: 0.0066s
Radius:6 1958.8380s 7.3746s first: 0.0272s
second: 0.0071s
Radius:10 5017.5250s 7.6009s first: 0.0294s
second: 0.0063s
Radius:20 8.1089s first: 0.0281s
second: 0.0073s
Box Blur & Better Box Blur & vImage
Size: 512 x 512 Device: iPad mini 2

30. Gaussian Blur
r=3 ,σ = 0.84089642
0.00000067 0.00002292 0.00019117 0.00038771 0.00019117 0.00002292 0.00000067
0.00002292 0.00078633 0.00655965 0.01330373 0.00655965 0.00078633 0.00002292
0.00019117 0.00655965 0.05472157 0.11098164 0.05472157 0.00655965 0.00019117
0.00038771 0.01330373 0.11098164 0.22508352 0.11098164 0.01330373 0.00038771
0.00019117 0.00655965 0.05472157 0.11098164 0.05472157 0.00655965 0.00019117
0.00002292 0.00078633 0.00655965 0.01330373 0.00655965 0.00078633 0.00002292
0.00000067 0.00002292 0.00019117 0.00038771 0.00019117 0.00002292 0.00000067

31. Gaussian Distribution
in one dimension in two dimensions

32. Gaussian function
in one dimension
in two dimensions

34. Core Image - Gaussian Blur
var context: CIContext!
let inputImage = CIImage(image: img)
let gaussianBlurFilter = CIFilter(name:"CIGaussianBlur", withInputParameters:
[kCIInputImageKey:inputImage,kCIInputRadiusKey:blurLevel])
let outputCIImage = gaussianBlurFilter.outputImage.imageByCroppingToRect(inputImage.extent())
context = CIContext(options:nil)
let cgimg = context.createCGImage(outputCIImage, fromRect: outputCIImage.extent())
let outputImage = UIImage(CGImage: cgimg)

35. Core Image - Gaussian Blur
Size: 512 x 512 Device: iPad mini 2
Gaussian Blur Speed
Level:1 0.1143s
Level:10 0.1192s
Level:100 0.1288s
Level:500 0.2334s
Level:680 0.1078s
Level:1000 0.1082s

36. Compare
Box Blur & Gaussian Blur
Box Blur Gaussian Blur

37. Compare
Box Blur & Gaussian Blur
Box Blur Gaussian Blur

38. Reference
http://en.wikipedia.org/wiki/Box_blur
http://en.wikipedia.org/wiki/Gaussian_blur
ACM SIGGRAPH@UIUC Fast Image Convolutions by: Wojciech Jarosz
http://blog.amritamaz.me/post/42203030076/understanding-box-blur
http://tech-algorithm.com/articles/boxfiltering/