feat(fourier): add frequency domain filters

- Add Low pass filter for image smoothing in frequency domain
- Add High pass filter for image sharpening in frequency domain

src/imgcv/filters/freq_domain.py

@@ -0,0 +1,148 @@
+import numpy as np
+from imgcv.fftpack.fft import fft2, ifft2, fftshift
+
+
+def low_pass_filter(img, cutoff, order=None, type="butterworth", return_img_fft=False):
+    """Apply low pass filter in the frequency domain to an image.
+    NOTE: Currently works only for square images and gray scale with size as power of 2.
+
+    Args:
+        img (np.ndarray): Input image to apply low pass filter.
+        cutoff (int): Cutoff frequency of the filter.
+        order (int, optional): Order of the Butterworth filter. Defaults to None. If None, order is set to 1.
+        type (str, optional): Type of the filter. Choose one of 'ideal', 'butterworth', 'gaussian'. Defaults to "butterworth".
+        return_img_fft (bool, optional): If True, return the filtered image in the frequency domain along with the original image in the frequency domain. Defaults to False.
+
+    Raises:
+        ValueError: If input image is not a numpy array.
+        ValueError: If input image is not 2D.
+        ValueError: If cutoff frequency is not an integer.
+        ValueError: If order is not an integer.
+        ValueError: If filter type is invalid.
+
+    Returns:
+        np.ndarray: Filtered image in the spatial domain.
+        (np.ndarray, np.ndarray): Filtered image in the frequency domain and the original image in the frequency domain (if return_img_fft is True)
+    """
+
+    if not isinstance(img, np.ndarray):
+        raise ValueError("Input image must be a numpy array.")
+
+    if img.ndim != 2:
+        raise ValueError("Input image must be 2D.")
+
+    if not isinstance(cutoff, int):
+        raise ValueError("Cutoff frequency must be an integer.")
+
+    if order is not None and not isinstance(order, int):
+        raise ValueError("Order must be an integer.")
+
+    if type not in ["ideal", "butterworth", "gaussian"]:
+        raise ValueError(
+            "Invalid filter type. Choose one of 'ideal', 'butterworth', 'gaussian'."
+        )
+
+    if order is None and type == "butterworth":
+        order = 1
+
+    if img.ndim == 2:
+        M, N = img.shape
+        img_fft = fft2(img)
+        img_fft_shifted = fftshift(img_fft)
+
+        # create distance matrix
+        u = np.arange(-M // 2, M // 2)
+        v = np.arange(-N // 2, N // 2)
+        U, V = np.meshgrid(u, v)
+        D = np.sqrt(U**2 + V**2)
+
+        H = np.zeros((M, N))
+
+        if type == "ideal":
+            H[D <= cutoff] = 1
+        elif type == "butterworth":
+            H = 1 / (1 + (D / cutoff) ** (2 * order))
+        elif type == "gaussian":
+            H = np.exp(-(D**2) / (2 * cutoff**2))
+
+        img_fft_filtered = img_fft_shifted * H
+
+        if return_img_fft:
+            return (img_fft_filtered, img_fft_shifted)
+
+        else:
+            img_filtered = np.abs(ifft2(img_fft_filtered))
+            return img_filtered
+
+
+def high_pass_filter(img, cutoff, order=None, type="butterworth", return_img_fft=False):
+    """Apply high pass filter in the frequency domain to an image.
+    NOTE: Currently works only for square images and gray scale with size as power of 2.
+
+    Args:
+        img (np.ndarray): Input image to apply high pass filter.
+        cutoff (int): Cutoff frequency of the filter.
+        order (int, optional): Order of the Butterworth filter. Defaults to None. If None, order is set to 1.
+        type (str, optional): Type of the filter. Choose one of 'ideal', 'butterworth', 'gaussian'. Defaults to "butterworth".
+        return_img_fft (bool, optional): If True, return the filtered image in the frequency domain along with the original image in the frequency domain. Defaults to False.
+
+    Raises:
+        ValueError: If input image is not a numpy array.
+        ValueError: If input image is not 2D.
+        ValueError: If cutoff frequency is not an integer.
+        ValueError: If order is not an integer.
+        ValueError: If filter type is invalid.
+
+    Returns:
+        np.ndarray: Filtered image in the spatial domain.
+        (np.ndarray, np.ndarray): Filtered image in the frequency domain and the original image in the frequency domain (if return_img_fft is True)
+    """
+
+    if not isinstance(img, np.ndarray):
+        raise ValueError("Input image must be a numpy array.")
+
+    if img.ndim != 2:
+        raise ValueError("Input image must be 2D.")
+
+    if not isinstance(cutoff, int):
+        raise ValueError("Cutoff frequency must be an integer.")
+
+    if order is not None and not isinstance(order, int):
+        raise ValueError("Order must be an integer.")
+
+    if type not in ["ideal", "butterworth", "gaussian"]:
+        raise ValueError(
+            "Invalid filter type. Choose one of 'ideal', 'butterworth', 'gaussian'."
+        )
+
+    if order is None and type == "butterworth":
+        order = 1
+
+    if img.ndim == 2:
+        M, N = img.shape
+        img_fft = fft2(img)
+        img_fft_shifted = fftshift(img_fft)
+
+        # create distance matrix
+        u = np.arange(-M // 2, M // 2)
+        v = np.arange(-N // 2, N // 2)
+        U, V = np.meshgrid(u, v)
+        D = np.sqrt(U**2 + V**2)
+
+        H = np.zeros((M, N))
+
+        if type == "ideal":
+            H[D > cutoff] = 1
+        elif type == "butterworth":
+            H = 1 / (1 + (cutoff / D) ** (2 * order))
+        elif type == "gaussian":
+            H = 1 - np.exp(-(D**2) / (2 * cutoff**2))
+
+        img_fft_filtered = img_fft_shifted * H
+
+        if return_img_fft:
+            return (img_fft_filtered, img_fft_shifted)
+
+        else:
+            img_filtered = np.abs(ifft2(img_fft_filtered))
+            return img_filtered