Expected behavior when using CIAdditionCompositing to add pure black?
I am attempting to understand how CIAdditionCompositing works.
As part of my testing, I have created a square mid-gray image:
and a square black image:
When I combined these two square images using a CIAdditionCompositing patch, I expected to see a gray square whose color matched the original mid-gray square exactly (because all color components of the black image have value 0). However, the final result is actually brighter than the original gray image:
I don't understand how this result is produced. What am I misunderstanding about how CIAdditionCompositing works?
Solution
So here is how I experimented with this. I generated images using Python PIL and numpy using below
from PIL import Image
import numpy as np
np.zeros(shape=(1,1,4))
for i in range(0, 176):
data[0][0] = [i, i, i, 255]
Image.fromarray(data).save("{}.png".format(i))
Then I wrote a XCode code to check your filter
let folder = "/Users/tarun.lalwani/Desktop/tarunlalwani.com/tarunlalwani/workshop/ub16/so/imagecompose/PS/"
let black_png = folder + "1.png";
let black_image = CIImage(image: UIImage(contentsOfFile: black_png)!)
for index in 1...175 {
let grey_png = folder + String(index) + ".png";
let grey_image = CIImage(image: UIImage(contentsOfFile: grey_png)!)
let combined_image = CIFilter(name: "CIAdditionCompositing", withInputParameters: ["inputImage":black_image!, "inputBackgroundImage":grey_image])
let context = CIContext() // Prepare for create CGImage
let cgimg = context.createCGImage((combined_image?.outputImage)!, from: (combined_image?.outputImage?.extent)!)
let output = UIImage(cgImage: cgimg!)
if let data = UIImagePNGRepresentation(output) {
do {
try data.write(to: (URL(fileURLWithPath: folder + "output" + String(index) + ".png")))
} catch {
print("Unexpected error: \(error).")
}
}
}
And then I ran below code in python to print the pixel values
for i in range(1, 176):
data = np.array(Image.open("output{}.png".format(i)))
print (data[0][0][0])
After that I plotted them all in an excel sheet. And here is my observation
- If sum of pixels from both images is > 255 then the final pixel value is 255
- If sum of pixels is less than 16 then no delta is added to the pixels
- If sum of the pixels is > 16 then some delta is added
Now the delta that I added is nearly equivalent to ROUNDUP((<sum of pixels>-16)/2-1,0). I say nearly because I could workout an 100% exact formula
So if A is the background image and B is the foreground image then below is the data from excel. The excel formula that I used was IF(ROUNDUP((D2-16)/2-1,0) <0, 0,ROUNDUP((D2-16)/2-1,0) )
+-------+-------+-------+-------+-------+---------+-------+
| A | B | C | A+B | A+B-C | Formula | E |
+-------+-------+-------+-------+-------+---------+-------+
| 1 | 1 | 2 | 2 | 0 | 0 | 0 |
| 2 | 1 | 3 | 3 | 0 | 0 | 0 |
| 3 | 1 | 4 | 4 | 0 | 0 | 0 |
| 4 | 1 | 5 | 5 | 0 | 0 | 0 |
| 5 | 1 | 6 | 6 | 0 | 0 | 0 |
| 6 | 1 | 7 | 7 | 0 | 0 | 0 |
| 7 | 1 | 8 | 8 | 0 | 0 | 0 |
| 8 | 1 | 9 | 9 | 0 | 0 | 0 |
| 9 | 1 | 10 | 10 | 0 | 0 | 0 |
| 10 | 1 | 11 | 11 | 0 | 0 | 0 |
| 11 | 1 | 12 | 12 | 0 | 0 | 0 |
| 12 | 1 | 13 | 13 | 0 | 0 | 0 |
| 13 | 1 | 14 | 14 | 0 | 0 | 0 |
| 14 | 1 | 15 | 15 | 0 | 0 | 0 |
| 15 | 1 | 17 | 16 | 1 | 0 | -1 |
| 16 | 1 | 18 | 17 | 1 | 0 | -1 |
| 17 | 1 | 19 | 18 | 1 | 0 | -1 |
| 18 | 1 | 21 | 19 | 2 | 1 | -1 |
| 19 | 1 | 22 | 20 | 2 | 1 | -1 |
| 20 | 1 | 24 | 21 | 3 | 2 | -1 |
| 21 | 1 | 25 | 22 | 3 | 2 | -1 |
| 22 | 1 | 27 | 23 | 4 | 3 | -1 |
| 23 | 1 | 28 | 24 | 4 | 3 | -1 |
| 24 | 1 | 30 | 25 | 5 | 4 | -1 |
| 25 | 1 | 31 | 26 | 5 | 4 | -1 |
| 26 | 1 | 33 | 27 | 6 | 5 | -1 |
| 27 | 1 | 34 | 28 | 6 | 5 | -1 |
| 28 | 1 | 36 | 29 | 7 | 6 | -1 |
| 29 | 1 | 37 | 30 | 7 | 6 | -1 |
| 30 | 1 | 39 | 31 | 8 | 7 | -1 |
| 31 | 1 | 40 | 32 | 8 | 7 | -1 |
| 32 | 1 | 42 | 33 | 9 | 8 | -1 |
| 33 | 1 | 43 | 34 | 9 | 8 | -1 |
| 34 | 1 | 44 | 35 | 9 | 9 | 0 |
| 35 | 1 | 46 | 36 | 10 | 9 | -1 |
| 36 | 1 | 47 | 37 | 10 | 10 | 0 |
| 37 | 1 | 49 | 38 | 11 | 10 | -1 |
| 38 | 1 | 50 | 39 | 11 | 11 | 0 |
| 39 | 1 | 52 | 40 | 12 | 11 | -1 |
| 40 | 1 | 53 | 41 | 12 | 12 | 0 |
| 41 | 1 | 55 | 42 | 13 | 12 | -1 |
| 42 | 1 | 56 | 43 | 13 | 13 | 0 |
| 43 | 1 | 58 | 44 | 14 | 13 | -1 |
| 44 | 1 | 59 | 45 | 14 | 14 | 0 |
| 45 | 1 | 61 | 46 | 15 | 14 | -1 |
| 46 | 1 | 62 | 47 | 15 | 15 | 0 |
| 47 | 1 | 64 | 48 | 16 | 15 | -1 |
| 48 | 1 | 65 | 49 | 16 | 16 | 0 |
| 49 | 1 | 67 | 50 | 17 | 16 | -1 |
| 50 | 1 | 68 | 51 | 17 | 17 | 0 |
| 51 | 1 | 70 | 52 | 18 | 17 | -1 |
| 52 | 1 | 71 | 53 | 18 | 18 | 0 |
| 53 | 1 | 73 | 54 | 19 | 18 | -1 |
| 54 | 1 | 74 | 55 | 19 | 19 | 0 |
| 55 | 1 | 76 | 56 | 20 | 19 | -1 |
| 56 | 1 | 77 | 57 | 20 | 20 | 0 |
| 57 | 1 | 79 | 58 | 21 | 20 | -1 |
| 58 | 1 | 80 | 59 | 21 | 21 | 0 |
| 59 | 1 | 82 | 60 | 22 | 21 | -1 |
| 60 | 1 | 83 | 61 | 22 | 22 | 0 |
| 61 | 1 | 85 | 62 | 23 | 22 | -1 |
| 62 | 1 | 86 | 63 | 23 | 23 | 0 |
| 63 | 1 | 88 | 64 | 24 | 23 | -1 |
| 64 | 1 | 89 | 65 | 24 | 24 | 0 |
| 65 | 1 | 91 | 66 | 25 | 24 | -1 |
| 66 | 1 | 92 | 67 | 25 | 25 | 0 |
| 67 | 1 | 94 | 68 | 26 | 25 | -1 |
| 68 | 1 | 95 | 69 | 26 | 26 | 0 |
| 69 | 1 | 97 | 70 | 27 | 26 | -1 |
| 70 | 1 | 98 | 71 | 27 | 27 | 0 |
| 71 | 1 | 100 | 72 | 28 | 27 | -1 |
| 72 | 1 | 101 | 73 | 28 | 28 | 0 |
| 73 | 1 | 103 | 74 | 29 | 28 | -1 |
| 74 | 1 | 104 | 75 | 29 | 29 | 0 |
| 75 | 1 | 106 | 76 | 30 | 29 | -1 |
| 76 | 1 | 107 | 77 | 30 | 30 | 0 |
| 77 | 1 | 109 | 78 | 31 | 30 | -1 |
| 78 | 1 | 110 | 79 | 31 | 31 | 0 |
| 79 | 1 | 112 | 80 | 32 | 31 | -1 |
| 80 | 1 | 113 | 81 | 32 | 32 | 0 |
| 81 | 1 | 115 | 82 | 33 | 32 | -1 |
| 82 | 1 | 116 | 83 | 33 | 33 | 0 |
| 83 | 1 | 118 | 84 | 34 | 33 | -1 |
| 84 | 1 | 119 | 85 | 34 | 34 | 0 |
| 85 | 1 | 121 | 86 | 35 | 34 | -1 |
| 86 | 1 | 122 | 87 | 35 | 35 | 0 |
| 87 | 1 | 124 | 88 | 36 | 35 | -1 |
| 88 | 1 | 125 | 89 | 36 | 36 | 0 |
| 89 | 1 | 127 | 90 | 37 | 36 | -1 |
| 90 | 1 | 128 | 91 | 37 | 37 | 0 |
| 91 | 1 | 129 | 92 | 37 | 37 | 0 |
| 92 | 1 | 131 | 93 | 38 | 38 | 0 |
| 93 | 1 | 132 | 94 | 38 | 38 | 0 |
| 94 | 1 | 134 | 95 | 39 | 39 | 0 |
| 95 | 1 | 135 | 96 | 39 | 39 | 0 |
| 96 | 1 | 137 | 97 | 40 | 40 | 0 |
| 97 | 1 | 138 | 98 | 40 | 40 | 0 |
| 98 | 1 | 140 | 99 | 41 | 41 | 0 |
| 99 | 1 | 141 | 100 | 41 | 41 | 0 |
| 100 | 1 | 143 | 101 | 42 | 42 | 0 |
| 101 | 1 | 144 | 102 | 42 | 42 | 0 |
| 102 | 1 | 146 | 103 | 43 | 43 | 0 |
| 103 | 1 | 147 | 104 | 43 | 43 | 0 |
| 104 | 1 | 149 | 105 | 44 | 44 | 0 |
| 105 | 1 | 150 | 106 | 44 | 44 | 0 |
| 106 | 1 | 152 | 107 | 45 | 45 | 0 |
| 107 | 1 | 153 | 108 | 45 | 45 | 0 |
| 108 | 1 | 155 | 109 | 46 | 46 | 0 |
| 109 | 1 | 156 | 110 | 46 | 46 | 0 |
| 110 | 1 | 158 | 111 | 47 | 47 | 0 |
| 111 | 1 | 159 | 112 | 47 | 47 | 0 |
| 112 | 1 | 161 | 113 | 48 | 48 | 0 |
| 113 | 1 | 162 | 114 | 48 | 48 | 0 |
| 114 | 1 | 164 | 115 | 49 | 49 | 0 |
| 115 | 1 | 165 | 116 | 49 | 49 | 0 |
| 116 | 1 | 167 | 117 | 50 | 50 | 0 |
| 117 | 1 | 168 | 118 | 50 | 50 | 0 |
| 118 | 1 | 170 | 119 | 51 | 51 | 0 |
| 119 | 1 | 171 | 120 | 51 | 51 | 0 |
| 120 | 1 | 173 | 121 | 52 | 52 | 0 |
| 121 | 1 | 174 | 122 | 52 | 52 | 0 |
| 122 | 1 | 176 | 123 | 53 | 53 | 0 |
| 123 | 1 | 177 | 124 | 53 | 53 | 0 |
| 124 | 1 | 179 | 125 | 54 | 54 | 0 |
| 125 | 1 | 180 | 126 | 54 | 54 | 0 |
| 126 | 1 | 182 | 127 | 55 | 55 | 0 |
| 127 | 1 | 183 | 128 | 55 | 55 | 0 |
| 128 | 1 | 185 | 129 | 56 | 56 | 0 |
| 129 | 1 | 186 | 130 | 56 | 56 | 0 |
| 130 | 1 | 188 | 131 | 57 | 57 | 0 |
| 131 | 1 | 189 | 132 | 57 | 57 | 0 |
| 132 | 1 | 191 | 133 | 58 | 58 | 0 |
| 133 | 1 | 192 | 134 | 58 | 58 | 0 |
| 134 | 1 | 194 | 135 | 59 | 59 | 0 |
| 135 | 1 | 195 | 136 | 59 | 59 | 0 |
| 136 | 1 | 197 | 137 | 60 | 60 | 0 |
| 137 | 1 | 198 | 138 | 60 | 60 | 0 |
| 138 | 1 | 200 | 139 | 61 | 61 | 0 |
| 139 | 1 | 201 | 140 | 61 | 61 | 0 |
| 140 | 1 | 203 | 141 | 62 | 62 | 0 |
| 141 | 1 | 204 | 142 | 62 | 62 | 0 |
| 142 | 1 | 206 | 143 | 63 | 63 | 0 |
| 143 | 1 | 207 | 144 | 63 | 63 | 0 |
| 144 | 1 | 209 | 145 | 64 | 64 | 0 |
| 145 | 1 | 210 | 146 | 64 | 64 | 0 |
| 146 | 1 | 212 | 147 | 65 | 65 | 0 |
| 147 | 1 | 213 | 148 | 65 | 65 | 0 |
| 148 | 1 | 215 | 149 | 66 | 66 | 0 |
| 149 | 1 | 216 | 150 | 66 | 66 | 0 |
| 150 | 1 | 218 | 151 | 67 | 67 | 0 |
| 151 | 1 | 219 | 152 | 67 | 67 | 0 |
| 152 | 1 | 221 | 153 | 68 | 68 | 0 |
| 153 | 1 | 222 | 154 | 68 | 68 | 0 |
| 154 | 1 | 224 | 155 | 69 | 69 | 0 |
| 155 | 1 | 225 | 156 | 69 | 69 | 0 |
| 156 | 1 | 227 | 157 | 70 | 70 | 0 |
| 157 | 1 | 228 | 158 | 70 | 70 | 0 |
| 158 | 1 | 230 | 159 | 71 | 71 | 0 |
| 159 | 1 | 231 | 160 | 71 | 71 | 0 |
| 160 | 1 | 233 | 161 | 72 | 72 | 0 |
| 161 | 1 | 234 | 162 | 72 | 72 | 0 |
| 162 | 1 | 236 | 163 | 73 | 73 | 0 |
| 163 | 1 | 237 | 164 | 73 | 73 | 0 |
| 164 | 1 | 239 | 165 | 74 | 74 | 0 |
| 165 | 1 | 240 | 166 | 74 | 74 | 0 |
| 166 | 1 | 242 | 167 | 75 | 75 | 0 |
| 167 | 1 | 243 | 168 | 75 | 75 | 0 |
| 168 | 1 | 245 | 169 | 76 | 76 | 0 |
| 169 | 1 | 246 | 170 | 76 | 76 | 0 |
| 170 | 1 | 248 | 171 | 77 | 77 | 0 |
| 171 | 1 | 249 | 172 | 77 | 77 | 0 |
| 172 | 1 | 251 | 173 | 78 | 78 | 0 |
| 173 | 1 | 252 | 174 | 78 | 78 | 0 |
| 174 | 1 | 254 | 175 | 79 | 79 | 0 |
| 175 | 1 | 255 | 176 | 79 | 79 | 0 |
+-------+-------+-------+-------+-------+---------+-------+
So unfortunately, they do say they use the formula described in
https://keithp.com/~keithp/porterduff/p253-porter.pdf
But the delta function is custom. Also I believe the formula from that PDF will come into picture when there is a custom alpha channel in the image that you use
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