bilateral filter Algorithm
The bilateral filter algorithm is a non-linear, edge-preserving, and noise-reducing smoothing technique for images. It combines the advantages of two basic image processing filters: the Gaussian filter, which smooths the image while blurring the edges, and the median filter, which preserves the edges but does not smooth the image effectively. The bilateral filter works by averaging the pixel values in a local neighborhood, but it takes into account both the spatial distance and the intensity difference between the central pixel and its neighbors. This allows the filter to preserve sharp edges and fine details while still reducing noise and smoothing the image.
The main idea behind the bilateral filter algorithm is to use a weighted average of the surrounding pixel values, where the weights depend on both the spatial distance and the intensity difference between the central pixel and its neighbors. The spatial distance helps in giving more importance to the nearby pixels, ensuring that the filter does not mix pixels from different regions with different intensities. The intensity difference ensures that the filter does not mix pixels with significantly different intensities, which helps in preserving the edges. The bilateral filter can be applied to both grayscale and color images, and it has been widely used in various image processing tasks, such as denoising, detail enhancement, and tone mapping.
"""
Implementation of Bilateral filter
Inputs:
img: A 2d image with values in between 0 and 1
varS: variance in space dimension.
varI: variance in Intensity.
N: Kernel size(Must be an odd number)
Output:
img:A 2d zero padded image with values in between 0 and 1
"""
import cv2
import numpy as np
import math
import sys
def vec_gaussian(img: np.ndarray, variance: float) -> np.ndarray:
# For applying gaussian function for each element in matrix.
sigma = math.sqrt(variance)
cons = 1 / (sigma * math.sqrt(2 * math.pi))
return cons * np.exp(-((img / sigma) ** 2) * 0.5)
def get_slice(img: np.ndarray, x: int, y: int, kernel_size: int) -> np.ndarray:
half = kernel_size // 2
return img[x - half : x + half + 1, y - half : y + half + 1]
def get_gauss_kernel(kernel_size: int, spatial_variance: float) -> np.ndarray:
# Creates a gaussian kernel of given dimension.
arr = np.zeros((kernel_size, kernel_size))
for i in range(0, kernel_size):
for j in range(0, kernel_size):
arr[i, j] = math.sqrt(
abs(i - kernel_size // 2) ** 2 + abs(j - kernel_size // 2) ** 2
)
return vec_gaussian(arr, spatial_variance)
def bilateral_filter(
img: np.ndarray,
spatial_variance: float,
intensity_variance: float,
kernel_size: int,
) -> np.ndarray:
img2 = np.zeros(img.shape)
gaussKer = get_gauss_kernel(kernel_size, spatial_variance)
sizeX, sizeY = img.shape
for i in range(kernel_size // 2, sizeX - kernel_size // 2):
for j in range(kernel_size // 2, sizeY - kernel_size // 2):
imgS = get_slice(img, i, j, kernel_size)
imgI = imgS - imgS[kernel_size // 2, kernel_size // 2]
imgIG = vec_gaussian(imgI, intensity_variance)
weights = np.multiply(gaussKer, imgIG)
vals = np.multiply(imgS, weights)
val = np.sum(vals) / np.sum(weights)
img2[i, j] = val
return img2
def parse_args(args: list) -> tuple:
filename = args[1] if args[1:] else "../image_data/lena.jpg"
spatial_variance = float(args[2]) if args[2:] else 1.0
intensity_variance = float(args[3]) if args[3:] else 1.0
if args[4:]:
kernel_size = int(args[4])
kernel_size = kernel_size + abs(kernel_size % 2 - 1)
else:
kernel_size = 5
return filename, spatial_variance, intensity_variance, kernel_size
if __name__ == "__main__":
filename, spatial_variance, intensity_variance, kernel_size = parse_args(sys.argv)
img = cv2.imread(filename, 0)
cv2.imshow("input image", img)
out = img / 255
out = out.astype("float32")
out = bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
out = out * 255
out = np.uint8(out)
cv2.imshow("output image", out)
cv2.waitKey(0)
cv2.destroyAllWindows()
