BLUR FILTERHANPO

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Why?

i.Frame Exhibition

CamInstagram Path

Instagram

Path

Cam

What?

How?

Image Data

Pixel

     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

Image (2D array of pixels)

Naïve Box BlurBox blur - 3*3 Matrix of 1/9 * determinant matrix

11 1

11 1

11 1

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

Naïve Box BlurImage 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)

Calculate all PixelsSample image 4 x 3 pixels, radius is 1

Box BlurR:0 R:1 R:3

R:6 R:10 R:20

Edge Handling

Better Box BlurFor it to be fast you must implement it as an accumulator, not a convolution loop.

Image convolution - the convolution of a 2D image is O(n^2 * 2m)

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

Calculate all PixelsSample 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

R:0 R:1 R:3

R:6 R:10 R:20

Better Box Blur

CompareBox 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

Convolutionfor 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

Accelerate FrameworkConsists 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

vImageAccelerate 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

vImage BlurR:0 R:1 R:3

R:6 R:10 R:20

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

Gaussian Blur

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

r=3 ,σ = 0.84089642

Gaussian Distribution

in one dimension in two dimensions

Gaussian function

in one dimension

in two dimensions

Core Image - Gaussian Blurvar 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)

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

Size: 512 x 512 Device: iPad mini 2Core Image - Gaussian Blur

Compare

Box Blur Gaussian Blur

Box Blur & Gaussian Blur

Compare

Box Blur Gaussian Blur

Box Blur & Gaussian Blur

Referencehttp://en.wikipedia.org/wiki/Box_blurhttp://en.wikipedia.org/wiki/Gaussian_blurACM SIGGRAPH@UIUC Fast Image Convolutions by: Wojciech Jaroszhttp://blog.amritamaz.me/post/42203030076/understanding-box-blurhttp://tech-algorithm.com/articles/boxfiltering/