Opencv_100问_第六章 (26-30)

使用双线插值放大图像1.5倍吧! 双线插值检查4邻域的像素点，并根据距离设置权值.虽然计算量的增加会延长处理时间，但可以有效抑制画质的劣化.

• 放大图像坐标(x',y除以放大率a,获得相应原始图像的坐标 floor(x'/a,y'/a). '
• 图像的坐标(x'/a,y'/a)四个邻域的坐标 I(x,y), I(x 1,y), I(x,y 1),I(x 1,y 1)

I(x,y)   I(x 1,y)  (x'/a,y'/a) I(x,y 1)  I(x 1,y 1) 

• 分别要求这四点和(x’/a,y’/a)权重根据距离设定： w = d / sum d

• 根据下公式放大后图像(x’,y)像素值：

dx = x'/a - x dy = y'/y - y I'(x',y') = (1-dx)(1-dy)I(x,y)   dx(1-dy)I(x 1,y)   (1-dx)dyI(x,y 1)   dxdyI(x 1,y 1) 

代码实现:

# @Time : 2022/6/11 16:59 # @Author : Fioman # @Phone : 13149920693 # @Tips : Talk is Cheap,Show me the code! ^_^^_^ from settings import *   def linear_interpolate(image, ax=1.1, ay=1.):
    H, W = image.shape[:2]
    aH = int(ay * H)
    aW = int(ax * H)

    # get position of original position
    y = np.arange(aH).repeat(aW).reshape(aH, -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.int0)
    iy = np.floor(y).astype(np.int0)

    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) * image[iy, ix] + dx * (1 - dy) * image[iy, ix + 1] + \
          (1 - dx) * dy * image[iy + 1, ix] + dx * dy * image[iy + 1, ix + 1]
    out = np.clip(out, 0, 255)
    out = out.astype(np.uint8)

    return out


if __name__ == '__main__':
    imagePath = os.path.join(OPENCV_100_Q_PATH,"color_02.bmp")
    imageOriginal = cv.imread(imagePath,cv.IMREAD_COLOR)
    out = linear_interpolate(imageOriginal,ax=1.5,ay=1.5)
    cv.imshow("Original",imageOriginal)
    cv.imshow("Out",out)
    cv.waitKey(0)

双三次插值是双线性插值的扩展,它使用的是邻域的16个像素进行插值.

I(x-1,y-1)  I(x,y-1)  I(x+1,y-1)  I(x+2,y-1)
I(x-1,y)    I(x,y)    I(x+1,y)    I(x+2,y)
I(x-1,y+1)  I(x,y+1)  I(x+1,y+1)  I(x+2,y+1)
I(x-1,y+2)  I(x,y+2)  I(x+1,y+2)  I(x+2,y+2)

各像素间的距离由下式决定:

dx1 = x'/a - (x-1) , dx2 = x'/a - x , dx3 = (x+1) - x'/a , dx4 = (x+2) - x'/a
dy1 = y'/a - (y-1) , dy2 = y'/a - y , dy3 = (y+1) - y'/a , dy4 = (y+2) - y'/a

由于距离的权重函数由以下函数取得,a在大部分时候取-1:

h(t) = { 
         (a+2)|t|^3 - (a+3)|t|^2 + 1    (when |t|<=1)
         a|t|^3 - 5a|t|^2 + 8a|t| - 4a  (when 1<|t|<=2)
         0                              (when 2<|t|) 

利用上面得到的权重,通过下面的式子扩大图像.将每个像素和权重的乘积之和除以权重的和.

I'(x', y') = (Sum{ 
        i=-1:2}{ 
        j=-1:2} I(x+i,y+j) * wxi * wyj) / Sum{ 
        i=-1:2}{ 
        j=-1:2} wxi * wyj

实现代码如下:

# @Time : 2022/6/13 10:48
# @Author : Fioman
# @Phone : 13149920693
# @Tips : Talk is Cheap,Show me the code! ^_^^_^
from settings import *

# Bicubic Interpolation (双三次插值算法)
def bicubic_interpolation(image,ax=1.,ay=1.):
    H,W,C = image.shape

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

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

    # get positions of original image
    ix = np.floor(x).astype(np.int0)
    iy = np.floor(y).astype(np.int0)

    ix = np.minimum(ix,W-1)
    iy = np.minimum(iy,H-1)

    # get distance of each postion of original image
    dx2 = x- ix
    dy2 = y - iy
    dx1 = dx2 + 1
    dy1 = dy2    +1
    dx3 = 1 - dx2
    dy3 = 1 - dy2
    dx4 = 1 +dx3
    dy4 = 1 + dy3

    dxs = [dx1,dx2,dx3,dx4]
    dys = [dy1,dy2,dy3,dy4]

    # bi-cubic weight
    def weight(t):
        a = -1
        at = np.abs(t)
        w = np.zeros_like(t)
        ind = np.where(at <= 1)
        w[ind] = ((a+2) * np.power(at,3) - (a +3) * np.power(at,2) + 1)[ind]
        ind = np.where((at > 1) & (at <= 2))
        w[ind] = (a * np.power(at,3) - 5 * a * np.power(at,2) +8*a*at - 4 * a)[ind]
        return w

    wSum = np.zeros((aH,aW,C),dtype=np.float32)
    out = np.zeros((aH,aW,C),dtype=np.float32)

    # interpolation
    for j in range(-1,3):
        for i in range(-1,3):
            indX = np.minimum(np.maximum(ix + i,0),W-1)
            indY = np.minimum(np.maximum(iy+j,0),H-1)

            wx = weight(dxs[i+1])
            wy = weight(dys[j+1])
            wx = np.repeat(np.expand_dims(wx,axis=-1),3,axis=-1)
            wy = np.repeat(np.expand_dims(wy,axis=-1),3,axis=-1)

            wSum += wx * wy
            out += wx*wy*image[indY,indX]

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

if __name__ == '__main__':
    imagePath = os.path.join(OPENCV_100_Q_PATH,"color_02.bmp")
    imageOriginal = cv.imread(imagePath,cv.IMREAD_COLOR)
    out = bicubic_interpolation(imageOriginal,1.5,1.5)
    cv.imshow("Original",imageOriginal)
    cv.imshow("BicubicRes",out)
    cv.waitKey(0)

平移操作可以这么去看待:

1. 使用仿射变换,将图片在x方向上放大1.3倍,在y方向上缩小至原来的0.8.
2. 在上面的条件下,同时在x方向上向右平移30(+30),在y方向上向上平移30(-30).

代码实现: