OpenCV 图像尺寸缩放时采用：

cv2.resize(src, dsize[, dst[, fx[, fy[, interpolation]]]])

其中，

插值方式可选：

通常的，缩小使用cv.INTER_AREA，放缩使用cv.INTER_CUBIC(较慢)和cv.INTER_LINEAR(较快效果也不错).默认情况下，所有的放缩都使用cv.INTER_LINEAR.

1. OpenCV 最近邻插值

原文：Opencv 最邻近插值 - 2020.02.17

Opencv最近邻插值在图像放大时补充的像素取最临近的像素的值.由于方法简单，所以处理速度很快，但是放大图像画质劣化明显.

如图，原始图像 $I$ ，放大后图像 $I'$，假设放大率为 $\alpha$，则最近邻插值公式为：

$$ I' (x, y) = I([\frac{x}{\alpha}], [\frac{y}{a}]) $$

1.1. Python 实现

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

# Nereset Neighbor interpolation
def nn_interpolate(img, ax=1, ay=1):
    H, W, C = img.shape

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

    y = np.arange(aH).repeat(aW).reshape(aW, -1)
    x = np.tile(np.arange(aW), (aH, 1))
    y = np.round(y / ay).astype(np.int)
    x = np.round(x / ax).astype(np.int)

    out = img[y,x]
    out = out.astype(np.uint8)

    return out

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

# Nearest Neighbor
out = nn_interpolate(img, ax=1.5, ay=1.5)

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

1.2. C++ 实现

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


// nearest nieghbor
cv::Mat nearest_neighbor(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;

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

  // nearest neighbor interpolation
  for (int y = 0; y < resized_height; y++){
    y_before = (int)round(y / ry);
    y_before = fmin(y_before, height - 1);

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

      // assign pixel to new position
      for (int c = 0; c < channel; c++){
          out.at<cv::Vec3b>(y, x)[c] = img.at<cv::Vec3b>(y_before, x_before)[c];
      }
    }
  }

  return out;
}


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

  // nearest neighbor
  cv::Mat out = nearest_neighbor(img, 1.5, 1.5);

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

  return 0;
}

2. OpenCV 双线性插值

原文：Opencv 双线性插值- 2020.02.17

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] - 放大后图像坐标为 $(x', y')$，放大率为 $\alpha$，则对应的原图像坐标为 $([\frac{x'}{\alpha}], [\frac{y'}{\alpha}])$.

[2] - 求原图像的像素坐标 $([\frac{x'}{\alpha}], [\frac{y'}{\alpha}])$ 周围 4 邻域的像素坐标 $I(x, y), I(x+1, y), I(x, y+1), I(x+1, y+1)$:

[3] - 分别求这 4 个点与 $([\frac{x'}{\alpha}], [\frac{y'}{\alpha}])$ 的距离，根据距离设置权重：$w = \frac{d}{\sum d}$.

[4] - 根据下面公式求得放大后图像 $(x', y')$ 处的像素值：

$$ d_x = \frac{x'}{\alpha} -x $$

$$ d_y = \frac{y'}{\alpha} - y $$

$$ I'(x', y') = (1 - d_x)(1 - d_y) I(x, y) + d_x(1 - d_y) I(x+1, y) + (1 - d_x)d_y I(x, y+1) + d_x d_y I(x+1, y+1) $$

2.1. 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)
    #y = np.tile(np.arange(aH), (aW, 1)).transpose()
    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.imwrite("out.jpg", out)

2.2. 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;
}