---
title: Digital Image Processing Assignment I
tags:
  - C/C++
  - Course Project
id: "3418"
categories:
  - - Coding
    - Digital Image Processing
date: 2019-09-19 23:15:31
---

### Main Contents

- Read a color bmp;
- RGB->YUV;
- Color to gray: gray=Y in YUV color space;
- Rearrange gray intensity to lie between [0,255];
- Write a grayscale bmp;
- Change the luminance value Y;
- YUV->RGB;
- Write a color bmp.

### Step One: BMP File Structure

A common BMP file is comprised of four part: image file header, image information header, palette and image data.

The image file header is a struct whose length is 14 bytes. Here gives its definition,

```c
typedef struct tagBITMAPFILEHEADER {
    WORD bfType;
    DWORD bfSize;
    WORD bfReserved1;
    WORD bfReserved2;
    DWORD bfOffBits;
} BITMAPFILEHEADER;
```

and the explanation for every variable.

- bfType: must always be set to 'BM' to declare that this is a .bmp-file;
- bfSize: specifies the size of the file in bytes;
- bfReserved1: must always be set to zero;
- bfReserved2: must always be set to zero;
- bfOffBits: specifies the offset from the beginning of the file to the bitmap data.

The image information header is also a struct, while its length is 40 bytes. The definition

```c
typedef struct tagBITMAPINFOHEADER {
    DWORD biSize;
    LONG biWidth;
    LONG biHeight;
    WORD biPlanes;
    WORD biBitCount
    DWORD biCompression;
    DWORD biSizeImage;
    LONG biXPelsPerMeter;
    LONG biYPelsPerMeter;
    DWORD biClrUsed;
    DWORD biClrImportant;
} BITMAPINFOHEADER;
```

The explanation

- biSize: number of bytes to define BITMAPINFORHEADER structure;
- biWidth: image width (number of pixels);
- biHeight: image height (number of pixels), note that if it's a positive number, the image is inverted, otherwise upright;
- biPlanes: number of planes, should always be 1;
- biBitCount: bits per pixel, which may be 1, 4, 8, 16, 24, 32;
- biCompression: compression type, only non-compression(BI_RGB) is discussed here;
- biSizeImage: image size with bytes, when biCompression is BI_RGB, biSizeImage is 0;
- biXPelsPerMeter: horizontal resolution, pixels per meter;
- biYPelsPerMeter: vertical resolution, pixels per meter;
- biClrUsed: number of color indices used in the bitmap, when it's 0, all the palette items are used;
- biClrImportant: number of important color indices for image display, when it's 0, all items are important.

The palette has a series of RGBQUADs, which is defined like this.

```c
typedef struct tagRGBQUAD {
    uint8_t rgbBlue;
    uint8_t rgbGreen;
    uint8_t rgbRed;
    uint8_t rgbReserved;
} RGBQUAD;
```

Note that the order of the color is **blue, green, and red**, not the reverse. The number of RGBQUADs is decided by biBitCount and biClrUsed.

Next we need to define BITMAPINFO.

```c
typedef struct tagBITMAPINFO {
    BITMAPINFOHEADER bmiHeader;
    RGBQUAD bmiColors[1];
} BITMAPINFO;
```

As we know nothing about the number of RGBQUADs an image uses, the BITMAPINFO should be defined as **a pointer** so that right amount of memory can be allocated to it.

The image data contains color of all pixels, and every biBitCount bit(s) represents a pixel.

At last, we define a struct to storage a full BMP image.

```c
typedef struct tagBITMAP {
    BITMAPFILEHEADER bmHeader;
    BITMAPINFO *bmInfo;
    uint32_t bmInfoSize;
    uint32_t bmBytesPerRow;
    uint8_t bmBytesPerPel;
    uint8_t *bmData;
} BITMAP;
```

When defining the two structs, we need to add a line `#pragma pack(push, 1)` to **avoid struct padding**.

### Step Two: Read/Write a BMP File

A BMP file is a binary file, so we need to add `"b"` to the second parameter when using `fopen`.

Another important thing is that the number of bytes in one row must always be adjusted to fit into the border of a multiple of four, and we need to calculate how many bytes are there in one row.

For convenience, we define an initialize function, which receives bmHeader and bmInfo, and initializes other variables.

```c
// given bmHeader and bmInfo, initialize others
void init_bmp(BITMAP *bmImg) {
    BITMAPINFOHEADER *bmiHeader = &(bmImg->bmInfo->bmiHeader);
    bmImg->bmBytesPerRow = ((bmiHeader->biWidth * bmiHeader->biBitCount + 31) >> 5) << 2;
    bmImg->bmBytesPerPel = bmiHeader->biBitCount >> 3;
    bmImg->bmData = (uint8_t *) malloc(bmImg->bmBytesPerRow * bmiHeader->biHeight);
}
```

The read function is showed below.

```c
// read a BMP from file
void read_bmp(BITMAP *bmImg, char *filepath) {
    FILE *fiInImg = fopen(filepath, "rb");
    BITMAPINFOHEADER bmiHeader;
    fread(&(bmImg->bmHeader), sizeof(BITMAPFILEHEADER), 1, fiInImg);
    fread(&bmiHeader, sizeof(BITMAPINFOHEADER), 1, fiInImg);
    // if biBitCount is less than 16, use all the palette, otherwise do not use palette
    if (bmiHeader.biBitCount < 16) {
        bmImg->bmInfoSize = sizeof(BITMAPINFOHEADER) + (sizeof(RGBQUAD) << bmiHeader.biBitCount);
    } else {
        bmImg->bmInfoSize = sizeof(BITMAPINFOHEADER);
    }
    bmImg->bmInfo = (BITMAPINFO *) malloc(bmImg->bmInfoSize);
    bmImg->bmInfo->bmiHeader = bmiHeader;
    if (bmiHeader.biBitCount < 16) {
        fread(bmImg->bmInfo->bmiColors, sizeof(RGBQUAD), 1 << bmiHeader.biBitCount, fiInImg);
    }
    init_bmp(bmImg);
    fread(bmImg->bmData, bmImg->bmBytesPerRow, bmiHeader.biHeight, fiInImg);
    fclose(fiInImg);
}
```

The write function looks similar with the read function.

```c
// write a BMP to file
void write_bmp(BITMAP *bmImg, char *filepath) {
    FILE *fiOutImg = fopen(filepath, "wb");
    fwrite(&(bmImg->bmHeader), sizeof(BITMAPFILEHEADER), 1, fiOutImg);
    fwrite(bmImg->bmInfo, bmImg->bmInfoSize, 1, fiOutImg);
    fwrite(bmImg->bmData, bmImg->bmBytesPerRow, bmImg->bmInfo->bmiHeader.biHeight, fiOutImg);
    fclose(fiOutImg);
}
```

### Step Three: Change Color to Gray

To make things easier, we define a function to duplicate a BMP file,

```c
// duplicate a BMP
void copy_bmp(BITMAP *bmDes, BITMAP *bmSrc) {
    memcpy(bmDes, bmSrc, sizeof(BITMAP));
    bmDes->bmInfo = (BITMAPINFO *) malloc(bmSrc->bmInfoSize);
    memcpy(bmDes->bmInfo, bmSrc->bmInfo, bmSrc->bmInfoSize);
    BITMAPINFOHEADER *bmiHeader = &(bmSrc->bmInfo->bmiHeader);
    bmDes->bmData = (uint8_t *) malloc(bmSrc->bmBytesPerRow * bmiHeader->biHeight);
    memcpy(bmDes->bmData, bmSrc->bmData, bmSrc->bmBytesPerRow * bmiHeader->biHeight);
}
```

and a function to make sure the RGB value of a pixel lie between [0, 255].

```c
// make RGB value legal
uint8_t adjust(double val) {
    int16_t ret = (int16_t) (val + 0.5);
    return ret < 0 ? 0 : ret > 255 ? 255 : ret;
}
```

We need to change RGB to YUV first, as the grayscale is determined by Y value. The formula is

$$
\begin{bmatrix} 0.299 & 0.587 & 0.114 \\\\ -0.147 & -0.289 & 0.436 \\\\ 0.615 & -0.515 & -0.100 \end{bmatrix} \times \begin{bmatrix} R \\\\ G \\\\ B \end{bmatrix} = \begin{bmatrix} Y \\\\ U \\\\ V \end{bmatrix}
$$

```c
    // calculate YUV value
    double *bmYUV = (double *) malloc(sizeof(double) * bmImg.bmBytesPerRow * bmiHeader->biHeight);
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            uint8_t *B = &bmImg.bmData[pos];
            uint8_t *G = &bmImg.bmData[pos + 1];
            uint8_t *R = &bmImg.bmData[pos + 2];
            bmYUV[pos] = 0.299 * *R + 0.587 * *G + 0.114 * *B;
            bmYUV[pos + 1] = -0.147 * *R - 0.289 * *G + 0.436 * *B;
            bmYUV[pos + 2] = 0.615 * *R - 0.515 * *G - 0.100 * *B;
        }
    }
```

To change color to gray, we can simply make the R, G and B value of a pixel equal to its Y value. It would be more complex if we want to change it into an image with biBitCount equal to 8, because we need to set the palette manually.

One more step, rearrange gray intensity to lie between [0,255]. It's just a math problem. So the code

```c
    // color to gray
    BITMAP bmGray;
    bmGray.bmHeader = bmImg.bmHeader;
    bmGray.bmInfoSize = sizeof(BITMAPINFOHEADER) + (sizeof(RGBQUAD) << 8);
    bmGray.bmInfo = (BITMAPINFO *) malloc(bmGray.bmInfoSize);
    bmGray.bmInfo->bmiHeader = *bmiHeader;
    bmGray.bmInfo->bmiHeader.biBitCount = 8;
    for (int i = 0; i < 256; ++i) {
        RGBQUAD *rgb = &(bmGray.bmInfo->bmiColors[i]);
        rgb->rgbBlue = i;
        rgb->rgbGreen = i;
        rgb->rgbRed = i;
        rgb->rgbReserved = 0;
    }
    init_bmp(&bmGray);
    uint8_t min = 255, max = 0;
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            double *Y = &bmYUV[pos];
            if (*Y < min) {
                min = *Y;
            }
            if (*Y > max) {
                max = *Y;
            }
        }
    }
    // rearrange gray indensity
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            double *Y = &bmYUV[pos];
            uint32_t _pos = h * bmGray.bmBytesPerRow + w * bmGray.bmBytesPerPel;
            bmGray.bmData[_pos] = adjust(255 * (*Y - min) / (max - min));
        }
    }
```

### Step Four: Change the Luminance

The luminance is depend on Y value, too. What we need to do is just changing the Y value and applying the inverse formula below.

$$
\begin{bmatrix} 1.000 & 0.000 & 1.140 \\\\ 1.000 & -0.3946 & -0.5805 \\\\ 1.000 & 2.032 & -0.0005 \end{bmatrix} \times \begin{bmatrix} Y \\\\ U \\\\ V \end{bmatrix} = \begin{bmatrix} R \\\\ G \\\\ B \end{bmatrix}
$$

And the code is simple.

```c
    // change luminance
    BITMAP bmLight, bmDark;
    copy_bmp(&bmLight, &bmImg);
    copy_bmp(&bmDark, &bmImg);
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            double *Y = &bmYUV[pos];
            double *U = &bmYUV[pos + 1];
            double *V = &bmYUV[pos + 2];
            bmLight.bmData[pos] = adjust(*Y + 25 + 2.032 * *U - 0.0005 * *V);
            bmLight.bmData[pos + 1] = adjust(*Y + 25 - 0.3946 * *U - 0.5805 * *V);
            bmLight.bmData[pos + 2] = adjust(*Y + 25 + 1.140 * *V);
            bmDark.bmData[pos] = adjust(*Y - 50 + 2.032 * *U - 0.0005 * *V);
            bmDark.bmData[pos + 1] = adjust(*Y - 50 - 0.3946 * *U - 0.5805 * *V);
            bmDark.bmData[pos + 2] = adjust(*Y - 50 + 1.140 * *V);
        }
    }
```

### Step Five: Complete Source Code

#### bmp.h

```c
#ifndef _BMP_H_
#define _BMP_H_

#include <stdint.h>

#pragma pack(push, 1) // avoid struct padding

typedef struct tagBITMAPFILEHEADER {
    uint16_t bfType;
    uint32_t bfSize;
    uint16_t bfReserved1;
    uint16_t bfReserved2;
    uint32_t bfOffBits;
} BITMAPFILEHEADER;

typedef struct tagBITMAPINFOHEADER {
    uint32_t biSize;
    int32_t biWidth;
    int32_t biHeight;
    uint16_t biPlanes;
    uint16_t biBitCount;
    uint32_t biCompression;
    uint32_t biSizeImage;
    int32_t biXPelsPerMeter;
    int32_t biYPelsPerMeter;
    uint32_t biClrUsed;
    uint32_t biClrImportant;
} BITMAPINFOHEADER;

typedef struct tagRGBQUAD {
    uint8_t rgbBlue;
    uint8_t rgbGreen;
    uint8_t rgbRed;
    uint8_t rgbReserved;
} RGBQUAD;

typedef struct tagBITMAPINFO {
    BITMAPINFOHEADER bmiHeader;
    RGBQUAD bmiColors[1];
} BITMAPINFO;

typedef struct tagBITMAP {
    BITMAPFILEHEADER bmHeader;
    BITMAPINFO *bmInfo;
    uint32_t bmInfoSize;
    uint32_t bmBytesPerRow;
    uint8_t bmBytesPerPel;
    uint8_t *bmData;
} BITMAP;

#pragma pack(pop)

#endif
```

#### bmp.c

```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "bmp.h"

// given bmHeader and bmInfo, initialize others
void init_bmp(BITMAP *bmImg) {
    BITMAPINFOHEADER *bmiHeader = &(bmImg->bmInfo->bmiHeader);
    bmImg->bmBytesPerRow = ((bmiHeader->biWidth * bmiHeader->biBitCount + 31) >> 5) << 2;
    bmImg->bmBytesPerPel = bmiHeader->biBitCount >> 3;
    bmImg->bmData = (uint8_t *) malloc(bmImg->bmBytesPerRow * bmiHeader->biHeight);
}

// read a BMP from file
void read_bmp(BITMAP *bmImg, char *filepath) {
    FILE *fiInImg = fopen(filepath, "rb");
    BITMAPINFOHEADER bmiHeader;
    fread(&(bmImg->bmHeader), sizeof(BITMAPFILEHEADER), 1, fiInImg);
    fread(&bmiHeader, sizeof(BITMAPINFOHEADER), 1, fiInImg);
    // if biBitCount is less than 16, use all the palette, otherwise do not use palette
    if (bmiHeader.biBitCount < 16) {
        bmImg->bmInfoSize = sizeof(BITMAPINFOHEADER) + (sizeof(RGBQUAD) << bmiHeader.biBitCount);
    } else {
        bmImg->bmInfoSize = sizeof(BITMAPINFOHEADER);
    }
    bmImg->bmInfo = (BITMAPINFO *) malloc(bmImg->bmInfoSize);
    bmImg->bmInfo->bmiHeader = bmiHeader;
    if (bmiHeader.biBitCount < 16) {
        fread(bmImg->bmInfo->bmiColors, sizeof(RGBQUAD), 1 << bmiHeader.biBitCount, fiInImg);
    }
    init_bmp(bmImg);
    fread(bmImg->bmData, bmImg->bmBytesPerRow, bmiHeader.biHeight, fiInImg);
    fclose(fiInImg);
}

// duplicate a BMP
void copy_bmp(BITMAP *bmDes, BITMAP *bmSrc) {
    memcpy(bmDes, bmSrc, sizeof(BITMAP));
    bmDes->bmInfo = (BITMAPINFO *) malloc(bmSrc->bmInfoSize);
    memcpy(bmDes->bmInfo, bmSrc->bmInfo, bmSrc->bmInfoSize);
    BITMAPINFOHEADER *bmiHeader = &(bmSrc->bmInfo->bmiHeader);
    bmDes->bmData = (uint8_t *) malloc(bmSrc->bmBytesPerRow * bmiHeader->biHeight);
    memcpy(bmDes->bmData, bmSrc->bmData, bmSrc->bmBytesPerRow * bmiHeader->biHeight);
}

// write a BMP to file
void write_bmp(BITMAP *bmImg, char *filepath) {
    FILE *fiOutImg = fopen(filepath, "wb");
    fwrite(&(bmImg->bmHeader), sizeof(BITMAPFILEHEADER), 1, fiOutImg);
    fwrite(bmImg->bmInfo, bmImg->bmInfoSize, 1, fiOutImg);
    fwrite(bmImg->bmData, bmImg->bmBytesPerRow, bmImg->bmInfo->bmiHeader.biHeight, fiOutImg);
    fclose(fiOutImg);
}

// make RGB value legal
uint8_t adjust(double val) {
    int16_t ret = (int16_t) (val + 0.5);
    return ret < 0 ? 0 : ret > 255 ? 255 : ret;
}

int main(int argc, char *argv[]) {
    // read bmp file
    BITMAP bmImg;
    read_bmp(&bmImg, "original.bmp");
    BITMAPINFOHEADER *bmiHeader = &(bmImg.bmInfo->bmiHeader);

    // calculate YUV value
    double *bmYUV = (double *) malloc(sizeof(double) * bmImg.bmBytesPerRow * bmiHeader->biHeight);
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            uint8_t *B = &bmImg.bmData[pos];
            uint8_t *G = &bmImg.bmData[pos + 1];
            uint8_t *R = &bmImg.bmData[pos + 2];
            bmYUV[pos] = 0.299 * *R + 0.587 * *G + 0.114 * *B;
            bmYUV[pos + 1] = -0.147 * *R - 0.289 * *G + 0.436 * *B;
            bmYUV[pos + 2] = 0.615 * *R - 0.515 * *G - 0.100 * *B;
        }
    }

    // color to gray
    BITMAP bmGray;
    bmGray.bmHeader = bmImg.bmHeader;
    bmGray.bmInfoSize = sizeof(BITMAPINFOHEADER) + (sizeof(RGBQUAD) << 8);
    bmGray.bmInfo = (BITMAPINFO *) malloc(bmGray.bmInfoSize);
    bmGray.bmInfo->bmiHeader = *bmiHeader;
    bmGray.bmInfo->bmiHeader.biBitCount = 8;
    for (int i = 0; i < 256; ++i) {
        RGBQUAD *rgb = &(bmGray.bmInfo->bmiColors[i]);
        // to prove that the palette works well, play a small trick
        rgb->rgbBlue = (i >> 4) << 4;
        rgb->rgbGreen = (i >> 4) << 4;
        rgb->rgbRed = (i >> 4) << 4;
        rgb->rgbReserved = 0;
    }
    init_bmp(&bmGray);
    uint8_t min = 255, max = 0;
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            double *Y = &bmYUV[pos];
            if (*Y < min) {
                min = *Y;
            }
            if (*Y > max) {
                max = *Y;
            }
        }
    }
    // rearrange gray indensity
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            double *Y = &bmYUV[pos];
            uint32_t _pos = h * bmGray.bmBytesPerRow + w * bmGray.bmBytesPerPel;
            bmGray.bmData[_pos] = adjust(255 * (*Y - min) / (max - min));
        }
    }
    write_bmp(&bmGray, "gray.bmp");

    // change luminance
    BITMAP bmLight, bmDark;
    copy_bmp(&bmLight, &bmImg);
    copy_bmp(&bmDark, &bmImg);
    for (uint32_t h = 0; h < bmiHeader->biHeight; ++h) {
        for (uint32_t w = 0; w < bmiHeader->biWidth; ++w) {
            uint32_t pos = h * bmImg.bmBytesPerRow + w * bmImg.bmBytesPerPel;
            double *Y = &bmYUV[pos];
            double *U = &bmYUV[pos + 1];
            double *V = &bmYUV[pos + 2];
            bmLight.bmData[pos] = adjust(*Y + 25 + 2.032 * *U - 0.0005 * *V);
            bmLight.bmData[pos + 1] = adjust(*Y + 25 - 0.3946 * *U - 0.5805 * *V);
            bmLight.bmData[pos + 2] = adjust(*Y + 25 + 1.140 * *V);
            bmDark.bmData[pos] = adjust(*Y - 50 + 2.032 * *U - 0.0005 * *V);
            bmDark.bmData[pos + 1] = adjust(*Y - 50 - 0.3946 * *U - 0.5805 * *V);
            bmDark.bmData[pos + 2] = adjust(*Y - 50 + 1.140 * *V);
        }
    }
    write_bmp(&bmLight, "light.bmp");
    write_bmp(&bmDark, "dark.bmp");

    return 0;
}
```
