In this problem you will be implementing the 2D convolution algorithm that is usually used in image processing applications. For example, 2D convolution is used to implement image filters in your favorite social media application and to detect objects using machine learning.

A straightforward implementation of 2D convolution in C consists of deeply nested for loops:

// Initialization int fx [10][10] ={ {183, 207, 128, 30, 109, 0, 14, 52, 15, 210}, {228, 76, 48, 82, 179, 194, 22, 168, 58, 116}, {228, 217, 180, 181, 243, 65, 24, 127, 216, 118}, {64, 210, 138, 104, 80, 137, 212, 196, 150, 139}, {155, 154, 36, 254, 218, 65, 3, 11, 91, 95}, {219, 10, 45, 193, 204, 196, 25, 177, 188, 170}, {189, 241, 102, 237, 251, 223, 10, 24, 171, 71}, {0, 4, 81, 158, 59, 232, 155, 217, 181, 19}, {25, 12, 80, 244, 227, 101, 250, 103, 68, 46}, {136, 152, 144, 2, 97, 250, 47, 58, 214, 51} }; // 2D Image int kx [5][5] = { {1, 1, 0, -1, -1}, {0, 1, 0, -1, 0}, {0, 0, 1, 0, 0}, {0, -1, 0, 1, 0}, {-1, -1, 0, 1, 1} }; // Kernel int gx [10][10]; // Output Result int iw = 10; // Image Width = 10 int ih = 10; // Image Height = 10 int kw = 5; // Kernel Width = 5 int kh = 5; // Kernel Height = 5

int ksw = 2; // Kernel Width Stride = (Kernel Width-1)/2 int khw = 2; // Kernel Height Stride = (Kernel Height-1)/2

// 2D Convolution Algorithm for (int y = 0; y < ih ; y++) {

for (int x = 0; x < iw ; x++) {

int sum = 0;

for (int i = 0; i < kw ; i++) {

for (int j = 0; j < kh ; j++) {

int temp1 = x+j -ksw;

int temp2 = y+i -khw;

if (temp1>=0 && temp1<=9 && temp2>=0 && temp2<=9)

sum = sum + kx[j][i] * fx [temp1][temp2];

}

}

gx[x][y] = sum;

}

} /* Output: Array = { {656 ,160 ,113 ,72 ,-51 ,-430 ,23 ,333 ,-70 ,-191 }, {586 ,261 ,99 ,33 ,200 ,294 ,161 ,299 ,-378 ,-431}, {217 ,631 ,482 ,311 ,86 ,-31 ,-30 ,-64 ,148 ,-9}, {-68 ,256 ,485 ,319 ,-96 ,17 ,208 ,271 ,285 ,125}, {-99 ,-77 ,404 ,691 ,354 ,-427 ,-389 ,0 ,211 ,205}, {43 ,103 ,244 ,497 ,420 ,101 ,-142 ,123 ,67 ,38}, {85 ,660 ,344 ,199 ,571 ,838 ,38 ,-468 ,-408 ,9 }, {12 ,137 ,-40 ,-138 ,98 ,697 ,316 ,-295 ,55 ,215}, {-170 ,-211 ,-282 ,88 ,507 ,409 ,352 ,235 ,222 ,208}, {39 ,-142 ,-301 ,-351 ,92 ,72 ,-62 ,427 ,624 ,517}, } */

You may assume that the input image and kernel are square.

Exercise

1. Write an ARM V7 assembly program that implements 2D convolution. Note that fx, image and kernel sizes, are all parameters passed to the program.