我试图在C语言中实现一个正、反离散余弦变换(DCT)。代码是通过DCT()函数将单个像素输入块转换为变换矩阵,然后通过IDCT()函数返回原始像素值。请参阅所附代码。我从idct输出的是244161244116等的连续值。从idct值来看,我的程序似乎不工作。有人能帮我一下,让我知道在每一个功能之后我应该期待什么样的结果吗?显然,在idct之后,我应该更接近原始的输入矩阵。
谢谢

 # include <stdio.h>
 # define PI 3.14

void dct(float [][]);       // Function prototypes
void idct(float [][]);     // Function prototypes

void dct(float inMatrix[8][8]){

    double dct,
    Cu,
    sum,
    Cv;

    int i,
    j,
    u,
    h = 0,
    v;

    FILE * fp = fopen("mydata.csv", "w");

    float dctMatrix[8][8],
    greyLevel;

    for (u = 0; u < 8; ++u) {
        for (v = 0; v < 8; ++v) {

            if (u == 0) {
                Cu = 1.0 / sqrt(2.0);
            } else {
                Cu = 1.0;
            }

            if (v == 0) {
                Cv = 1.0 / sqrt(2.0);
            } else {
                Cu = (1.0);
            }

            sum = 0.0;

            for (i = 0; i < 8; i++) {
                for (j = 0; j < 8; j++) {

                    // Level around 0
                    greyLevel = inMatrix[i][j];

                    dct = greyLevel * cos((2 * i + 1) * u * PI / 16.0) *
                        cos((2 * j + 1) * v * PI / 16.0);

                    sum += dct;

                }
            }
            dctMatrix[u][v] = 0.25 * Cu * Cv * sum;
            fprintf(fp, "\n %f", dctMatrix[u][v]);
        }
        fprintf(fp, "\n");
    }
    idct(dctMatrix);
 }

void idct(float dctMatrix[8][8]){

    double idct,
    Cu,
    sum,
    Cv;

    int i,
    j,
    u,
    v;

    float idctMatrix[8][8],
    greyLevel;

    FILE * fp = fopen("mydata.csv", "a");

    fprintf(fp, "\n Inverse DCT");

    for (i = 0; i < 8; ++i) {
        for (j = 0; j < 8; ++j) {

            sum = 0.0;

        for (u = 0; u < 8; u++) {
            for (v = 0; v < 8; v++) {

            if (u == 0) {
                Cu = 1.0 / sqrt(2.0);
            } else {
                Cu = 1.0;
              }

            if (v == 0) {
                Cv = 1.0 / sqrt(2.0);
            } else {
                Cu = (1.0);
              }

                    // Level around 0
                greyLevel = dctMatrix[u][v];

                idct = (greyLevel * cos((2 * i + 1) * u * PI / 16.0) *
                        cos((2 * j + 1) * v * PI / 16.0));

                sum += idct;

                }
            }
            idctMatrix[i][j] = 0.25 * Cu * Cv * sum;
            fprintf(fp, "\n %f", idctMatrix[i][j]);
        }
        fprintf(fp, "\n");
    }
 }


int main() {

   float
    testBlockA[8][8] = { {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255} },

    testBlockB[8][8] = {{255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255},
                        {255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255},
                        {255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255},
                        {255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255} };

    dct(testBlockB);
}

最佳答案

if语句的cv常量赋值中至少有两个输入错误:

    if (v == 0) {
        Cv = 1.0 / sqrt(2.0);
    } else {
        Cu = (1.0); // << this should be Cv = 1.0
    }

但是检查得不太好。使用关于余弦变换的german wikipedia,下面的代码可以工作…
我不想花时间搞清楚你是如何定义转换常数的。
我想您需要确保使用正确的常量和反函数:
#include <stdio.h>
#include <math.h>
#include <stdlib.h>

void dct(float **DCTMatrix, float **Matrix, int N, int M);
void write_mat(FILE *fp, float **testRes, int N, int M);
void idct(float **Matrix, float **DCTMatrix, int N, int M);
float **calloc_mat(int dimX, int dimY);
void free_mat(float **p);


float **calloc_mat(int dimX, int dimY){
    float **m = calloc(dimX, sizeof(float*));
    float *p = calloc(dimX*dimY, sizeof(float));
    int i;
    for(i=0; i <dimX;i++){
    m[i] = &p[i*dimY];

    }
   return m;
}

void free_mat(float **m){
  free(m[0]);
  free(m);
}

void write_mat(FILE *fp, float **m, int N, int M){

   int i, j;
   for(i =0; i< N; i++){
    fprintf(fp, "%f", m[i][0]);
    for(j = 1; j < M; j++){
       fprintf(fp, "\t%f", m[i][j]);
        }
    fprintf(fp, "\n");
   }
   fprintf(fp, "\n");
}

void dct(float **DCTMatrix, float **Matrix, int N, int M){

    int i, j, u, v;
    for (u = 0; u < N; ++u) {
        for (v = 0; v < M; ++v) {
        DCTMatrix[u][v] = 0;
            for (i = 0; i < N; i++) {
                for (j = 0; j < M; j++) {
                    DCTMatrix[u][v] += Matrix[i][j] * cos(M_PI/((float)N)*(i+1./2.)*u)*cos(M_PI/((float)M)*(j+1./2.)*v);
                }
            }
        }
    }
 }

void idct(float **Matrix, float **DCTMatrix, int N, int M){
    int i, j, u, v;

    for (u = 0; u < N; ++u) {
        for (v = 0; v < M; ++v) {
          Matrix[u][v] = 1/4.*DCTMatrix[0][0];
          for(i = 1; i < N; i++){
          Matrix[u][v] += 1/2.*DCTMatrix[i][0];
           }
           for(j = 1; j < M; j++){
          Matrix[u][v] += 1/2.*DCTMatrix[0][j];
           }

           for (i = 1; i < N; i++) {
                for (j = 1; j < M; j++) {
                    Matrix[u][v] += DCTMatrix[i][j] * cos(M_PI/((float)N)*(u+1./2.)*i)*cos(M_PI/((float)M)*(v+1./2.)*j);
                }
            }
        Matrix[u][v] *= 2./((float)N)*2./((float)M);
        }
    }
 }



int main() {

   float
    testBlockA[8][8] = { {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255},
                         {255, 255, 255, 255, 255, 255, 255, 255} },

    testBlockB[8][8] = {{255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255},
                        {255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255},
                        {255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255},
                        {255, 0, 255, 0, 255, 0, 255, 0},
                        {0, 255, 0, 255, 0, 255, 0, 255} };

    FILE * fp = fopen("mydata.csv", "w");
    int dimX = 8, dimY = 8;
    int i, j;

    float **testBlock = calloc_mat(dimX, dimY);
    float **testDCT = calloc_mat(dimX, dimY);
    float **testiDCT = calloc_mat(dimX, dimY);

    for(i = 0; i<dimX; i++){
      for(j = 0; j<dimY; j++){
        testBlock[i][j] = testBlockB[i][j];
      }
    }

    dct(testDCT, testBlock, dimX, dimY);
    write_mat(fp, testDCT, dimX, dimY);

    idct(testiDCT, testDCT, dimX, dimY);
    write_mat(fp, testiDCT, dimX, dimY);

    fclose(fp);
    free_mat(testBlock);
    free_mat(testDCT);
    free_mat(testiDCT);

    return 0;
}

编辑
离散余弦变换是基于wiki中公式dct-ii的积。
idct基于公式dct-iii与每个维度的归一化因子2/n的积(因为这与文中提到的dct-ii相反)。
编辑
我很确定在你的版本中,逆dct中的因子应该是sqrt(2),而不是1/sqrt(2)。

关于c - 离散余弦变换DCT实现C,我们在Stack Overflow上找到一个类似的问题:https://stackoverflow.com/questions/8310749/

10-11 23:06
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