# Projection Profile method

In Image Processing, projection profile refers to projection of sum of hits/positives along an axis from bi-dimensional image. Projection profile method is majorly used for segmentation of text objects present inside text documents.

Solution:

Note: Projection profile is calculated for a thresholded image or binarized image where a thresholded image is a grayscale image with pixel values as 0 or 255. Image pixels are replaced by 1 and 0 for pixel values 0 and 255 respectively.

Projection profile is calculated separately for different axis. Projection profile along vertical axis is called Vertical Projection profile. Vertical projection profile is calculated for every column as sum of all row pixel values inside the column. Horizontal Projection profile is the projection profile of a image along horizontal axis. Horizontal Projection profile is calculated for every row as sum of all column pixel values inside the row.

Code Implementation for Horizontal Projection Profile:

## C++

 `#include ` `using` `namespace` `std; ` ` `  `// Function to generate horizontal projection profile ` `vector<``int``> getHorizontalProjectionProfile( ` `    ``vector > image, ``int` `rows, ``int` `cols) ` `{ ` ` `  `    ``for` `(``int` `i = 0; i < rows; i++) ` `    ``{ ` `        ``for` `(``int` `j = 0; j < cols; j++) ` `        ``{ ` `            ``// Convert black spots to ones ` `            ``if` `(image[i][j] == 0) ` `            ``{ ` `                ``image[i][j] = 1; ` `            ``} ` `            ``// Convert white spots to zeros ` `            ``else` `if` `(image[i][j] == 255) ` `            ``{ ` `                ``image[i][j] = 0; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``vector<``int``> horizontal_projection(rows, 0); ` ` `  `    ``// Calculate sum of 1's for every row ` `    ``for` `(``int` `i = 0; i < rows; i++) ` `    ``{ ` `        ``// Sum all 1's ` `        ``for` `(``int` `j = 0; j < cols; j++) ` `        ``{ ` `            ``horizontal_projection[i] += image[i][j]; ` `        ``} ` `    ``} ` ` `  `    ``return` `horizontal_projection; ` `} ` `// Driver Function ` `int` `main() ` `{ ` `    ``int` `rows = 5, cols = 3; ` `    ``vector > image = { { 0, 0, 0 }, ` `        ``{ 0, 255, 255 }, ` `        ``{ 0, 0, 0 }, ` `        ``{ 0, 255, 255 }, ` `        ``{ 0, 0, 0 } ` `    ``}; ` ` `  `    ``vector<``int``> horizontal_projection = getHorizontalProjectionProfile( ` `                                            ``image, rows, cols); ` ` `  `for` `(``auto` `it : horizontal_projection) ` `    ``{ ` `        ``cout << it << ``" "``; ` `    ``} ` `    ``return` `0; ` `} `

## Python3

 `import` `numpy as np ` ` `  `# Function to generate horizontal projection profile ` `def` `getHorizontalProjectionProfile(image): ` ` `  `    ``# Convert black spots to ones ` `    ``image[image ``=``=` `0``]   ``=` `1` `    ``# Convert white spots to zeros ` `    ``image[image ``=``=` `255``] ``=` `0` ` `  `    ``horizontal_projection ``=` `np.``sum``(image, axis ``=` `1``)  ` ` `  `    ``return` `horizontal_projection ` ` `  ` `  `# Driver Function ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``rows ``=` `5` `    ``cols ``=` `3` `    ``image ``=` `np.array([[``0``, ``0``, ``0``], ` `            ``[``0``, ``255``, ``255``], ` `            ``[``0``, ``0``, ``0``], ` `            ``[``0``, ``255``, ``255``], ` `            ``[``0``, ``0``, ``0``]]) ` `     `  `    ``horizontal_projection ``=` `getHorizontalProjectionProfile(image.copy()) ` ` `  `    ``print``(``*``horizontal_projection) `

Output:

```3 1 3 1 3
```

Code Implementation for Vertical Projection Profile:

## C++

 `#include ` `using` `namespace` `std; ` ` `  `// Function to generate vertical projection profile ` `vector<``int``> getVerticalProjectionProfile( ` `    ``vector > image, ``int` `rows, ``int` `cols) ` `{ ` ` `  `    ``for` `(``int` `i = 0; i < rows; i++) ` `    ``{ ` `        ``for` `(``int` `j = 0; j < cols; j++) ` `        ``{ ` `            ``// Convert black spots to ones ` `            ``if` `(image[i][j] == 0) ` `            ``{ ` `                ``image[i][j] = 1; ` `            ``} ` `            ``// Convert white spots to zeros ` `            ``else` `if` `(image[i][j] == 255) ` `            ``{ ` `                ``image[i][j] = 0; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``vector<``int``> vertical_projection(cols, 0); ` ` `  `    ``// Calculate sum of 1's for every column ` `    ``for` `(``int` `j = 0; j < cols; j++) ` `    ``{ ` `        ``// Sum all 1's ` `        ``for` `(``int` `i = 0; i < rows; i++) ` `        ``{ ` `            ``vertical_projection[j] += image[i][j]; ` `        ``} ` `    ``} ` ` `  `    ``return` `vertical_projection; ` `} ` ` `  `// Driver Function ` `int` `main() ` `{ ` `    ``int` `rows = 5, cols = 3; ` `    ``vector > image = { { 0, 0, 0 }, ` `        ``{ 0, 255, 255 }, ` `        ``{ 0, 0, 0 }, ` `        ``{ 0, 255, 255 }, ` `        ``{ 0, 0, 0 } ` `    ``}; ` ` `  `    ``vector<``int``> vertical_projection = getVerticalProjectionProfile( ` `                                          ``image, rows, cols); ` ` `  `for` `(``auto` `it : vertical_projection) ` `    ``{ ` `        ``cout << it << ``" "``; ` `    ``} ` `    ``return` `0; ` `} `

## Python3

 `import` `numpy as np ` ` `  `# Function to generate vertical projection profile ` `def` `getVerticalProjectionProfile(image): ` ` `  `    ``# Convert black spots to ones  ` `    ``image[image ``=``=` `0``]   ``=` `1` `    ``# Convert white spots to zeros  ` `    ``image[image ``=``=` `255``] ``=` `0` ` `  `    ``vertical_projection ``=` `np.``sum``(image, axis ``=` `0``) ` ` `  `    ``return` `vertical_projection ` ` `  `# Driver Function ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``rows ``=` `5` `    ``cols ``=` `3` `    ``image ``=` `np.array([[``0``, ``0``, ``0``], ` `            ``[``0``, ``255``, ``255``], ` `            ``[``0``, ``0``, ``0``], ` `            ``[``0``, ``255``, ``255``], ` `            ``[``0``, ``0``, ``0``]]) ` ` `  `    ``vertical_projection ``=` `getVerticalProjectionProfile(image.copy()) ` ` `  `    ``print``(``*``vertical_projection) `

Output:

```5 3 3
```

Time Complexity: O(rows*columns)
Space Complexity: O(rows*columns)

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