.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/05_smoothing_splines/02_2d_image_smoothing.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_05_smoothing_splines_02_2d_image_smoothing.py>`
        to download the full example code or to run this example in your browser via Binder.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_05_smoothing_splines_02_2d_image_smoothing.py:


2D Image Smoothing
==================

We use the smooth module to smooth a 2D grayscale image,
with strong visible noise.

.. GENERATED FROM PYTHON SOURCE LINES 14-16

Imports
-------

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt
    from splineops.smoothing_splines.smoothing_spline import smoothing_spline_nd








.. GENERATED FROM PYTHON SOURCE LINES 22-24

2D Image Smoothing
------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-128

.. code-block:: Python


    from urllib.request import urlopen
    from PIL import Image

    def create_image():
        """
        Loads a real image and converts it to grayscale.
        """
        url = 'https://r0k.us/graphics/kodak/kodak/kodim06.png'
        with urlopen(url, timeout=10) as resp:
            # Force grayscale (L = luminance)
            img = Image.open(resp).convert('L')

        data = np.array(img, dtype=np.float64)
        data /= 255.0  # Normalize to [0, 1] grayscale

        return data

    def add_noise(img, snr_db):
        """
        Adds Gaussian noise to the image based on the desired SNR in dB.
        """
        signal_power = np.mean(img ** 2)
        sigma = np.sqrt(signal_power / (10 ** (snr_db / 10)))
        noise = np.random.randn(*img.shape) * sigma
        noisy_img = img + noise

        # Keep within [0, 1] for nicer display
        noisy_img = np.clip(noisy_img, 0.0, 1.0)

        return noisy_img

    def compute_snr(clean_signal, noisy_signal):
        """
        Compute the Signal-to-Noise Ratio (SNR).

        Parameters:
        clean_signal (np.ndarray): Original clean signal.
        noisy_signal (np.ndarray): Noisy signal.

        Returns:
        float: SNR value in decibels (dB).
        """
        signal_power = np.mean(clean_signal ** 2)
        noise_power = np.mean((noisy_signal - clean_signal) ** 2)
        snr = 10 * np.log10(signal_power / noise_power)
        return snr

    def demo_image():
        # Parameters
        lambda_ = 0.1   # Regularization parameter
        gamma = 2.0     # Order of the spline operator

        # Noise
        snr_db = 8.0

        # Load grayscale image
        img = create_image()

        # Add noise
        noisy_img = add_noise(img, snr_db)

        # Smooth the noisy image
        smoothed_img = smoothing_spline_nd(noisy_img, lambda_, gamma)

        # Clip for display and SNR computation
        smoothed_img = np.clip(smoothed_img, 0.0, 1.0)

        # Compute SNRs
        snr_noisy = compute_snr(img, noisy_img)
        snr_smooth = compute_snr(img, smoothed_img)
        snr_improvement = snr_smooth - snr_noisy

        print("Image:")
        print(f"SNR of noisy image: {snr_noisy:.2f} dB")
        print(f"SNR after smoothing: {snr_smooth:.2f} dB")
        print(f"SNR improvement: {snr_improvement:.2f} dB\n")

        # Visualization for image
        plt.figure(figsize=(12, 4))

        # Original grayscale image
        plt.subplot(1, 3, 1)
        plt.imshow(img, cmap='gray', vmin=0, vmax=1)
        plt.title('Original Grayscale Image')
        plt.axis('off')

        # Noisy image
        plt.subplot(1, 3, 2)
        plt.imshow(noisy_img, cmap='gray', vmin=0, vmax=1)
        plt.title(f'Noisy Image (SNR={snr_noisy:.2f} dB)')
        plt.axis('off')

        # Smoothed grayscale image
        plt.subplot(1, 3, 3)
        plt.imshow(smoothed_img, cmap='gray', vmin=0, vmax=1)
        plt.title(f'Smoothed Image (SNR={snr_smooth:.2f} dB)')
        plt.axis('off')

        plt.tight_layout()
        plt.show()

    # Run the image demo
    demo_image()



.. image-sg:: /auto_examples/05_smoothing_splines/images/sphx_glr_02_2d_image_smoothing_001.png
   :alt: Original Grayscale Image, Noisy Image (SNR=8.90 dB), Smoothed Image (SNR=15.17 dB)
   :srcset: /auto_examples/05_smoothing_splines/images/sphx_glr_02_2d_image_smoothing_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Image:
    SNR of noisy image: 8.90 dB
    SNR after smoothing: 15.17 dB
    SNR improvement: 6.27 dB






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.929 seconds)


.. _sphx_glr_download_auto_examples_05_smoothing_splines_02_2d_image_smoothing.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/splineops/splineops.github.io/main?urlpath=lab/tree/notebooks_binder/auto_examples/05_smoothing_splines/02_2d_image_smoothing.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 02_2d_image_smoothing.ipynb <02_2d_image_smoothing.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 02_2d_image_smoothing.py <02_2d_image_smoothing.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 02_2d_image_smoothing.zip <02_2d_image_smoothing.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_