Opencv 双线性插值

使用双线性插值将图像放大1.5倍吧！

双线性插值考察4邻域的像素点，并根据距离设置权值。虽然计算量增大使得处理时间变长，但是可以有效抑制画质劣化。

1. 放大后图像的座标(x’,y’)除以放大率a，可以得到对应原图像的座标(\lfloor \frac{x’}{a}\rfloor , \lfloor \frac{y’}{a}\rfloor)。

2. 求原图像的座标(\lfloor \frac{x’}{a}\rfloor , \lfloor \frac{y’}{a}\rfloor)周围4邻域的座标I(x,y)，I(x+1,y)，I(x,y+1)，I(x+1, y+1)：

   

3. 分别求这4个点与(\frac{x’}{a}, \frac{y’}{a})的距离，根据距离设置权重：w = \frac{d}{\sum\ d}

4. 根据下式求得放大后图像(x’,y’)处的像素值：
   d_x = \frac{x’}{a} – x\\ d_y = \frac{y’}{a} – y\\ I'(x’,y’) = (1-d_x)\ (1-d_y)\ I(x,y) + d_x\ (1-d_y)\ I(x+1,y) + (1-d_x)\ d_y\ I(x,y+1) + d_x\ d_y\ I(x+1,y+1)

python实现：

import cv2
import numpy as np
import matplotlib.pyplot as plt


# Bi-Linear interpolation
def bl_interpolate(img, ax=1., ay=1.):
    H, W, C = img.shape

    aH = int(ay * H)
    aW = int(ax * W)

    # get position of resized image
    y = np.arange(aH).repeat(aW).reshape(aW, -1)
    x = np.tile(np.arange(aW), (aH, 1))

    # get position of original position
    y = (y / ay)
    x = (x / ax)

    ix = np.floor(x).astype(np.int)
    iy = np.floor(y).astype(np.int)

    ix = np.minimum(ix, W-2)
    iy = np.minimum(iy, H-2)

    # get distance 
    dx = x - ix
    dy = y - iy

    dx = np.repeat(np.expand_dims(dx, axis=-1), 3, axis=-1)
    dy = np.repeat(np.expand_dims(dy, axis=-1), 3, axis=-1)

    # interpolation
    out = (1-dx) * (1-dy) * img[iy, ix] + dx * (1 - dy) * img[iy, ix+1] + (1 - dx) * dy * img[iy+1, ix] + dx * dy * img[iy+1, ix+1]

    out = np.clip(out, 0, 255)
    out = out.astype(np.uint8)

    return out


# Read image
img = cv2.imread("imori.jpg").astype(np.float)

# Bilinear interpolation
out = bl_interpolate(img, ax=1.5, ay=1.5)

# Save result
cv2.imshow("result", out)
cv2.waitKey(0)
cv2.imwrite("out.jpg", out)

c++实现：

#include <opencv2/core.hpp>
#include <opencv2/highgui.hpp>
#include <iostream>
#include <math.h>


// bilinear
cv::Mat bilinear(cv::Mat img, double rx, double ry){
  // get height and width
  int width = img.cols;
  int height = img.rows;
  int channel = img.channels();


  // get resized shape
  int resized_width = (int)(width * rx);
  int resized_height = (int)(height * ry);
  int x_before, y_before;
  double dx, dy;
  double val;

  // output image
  cv::Mat out = cv::Mat::zeros(resized_height, resized_width, CV_8UC3);

  // bi-linear interpolation
  for (int y = 0; y < resized_height; y++){
    y_before = (int)floor(y / ry);
    y_before = fmin(y_before, height - 1);
    dy = y / ry - y_before;

    for (int x = 0; x < resized_width; x++){
      x_before = (int)floor(x / rx);
      x_before = fmin(x_before, width - 1);
      dx = x / rx - x_before;

      // compute bi-linear
      for (int c = 0; c < channel; c++){
        val = (1. - dx) * (1. - dy) * img.at<cv::Vec3b>(y_before, x_before)[c] +
          dx * (1. - dy) * img.at<cv::Vec3b>(y_before, x_before + 1)[c] +
          (1. - dx) * dy * img.at<cv::Vec3b>(y_before + 1, x_before)[c] +
          dx * dy * img.at<cv::Vec3b>(y_before + 1, x_before)[c];

        // assign pixel to new position
        out.at<cv::Vec3b>(y, x)[c] = (uchar)val;
      }
    }
  }

  return out;
}


int main(int argc, const char* argv[]){
  // read image
  cv::Mat img = cv::imread("imori.jpg", cv::IMREAD_COLOR);

  // bilinear
  cv::Mat out = bilinear(img, 1.5, 1.5);

  //cv::imwrite("out.jpg", out);
  cv::imshow("answer", out);
  cv::waitKey(0);
  cv::destroyAllWindows();

  return 0;
}

输入：

输出：