`skimage.restoration._denoise:denoise_tv_chambolle`

source: /dev/scikit-image/src/skimage/restoration/_denoise.py :490

Signature

   def     denoise_tv_chambolle (    image    ,    weight    =  0.1   ,    eps    =  0.0002   ,    max_num_iter    =  200   ,  * ,     channel_axis    =  None     )

Summary

Perform total variation denoising in nD.

Extended Summary

Given $f$ , a noisy image (input data), total variation denoising (also known as total variation regularization) aims to find an image $u$ with less total variation than $f$ , under the constraint that $u$ remain similar to $f$ . This can be expressed by the Rudin--Osher--Fatemi (ROF) minimization problem:

u min i = 0 \sum N - 1 (∣ \nabla u_{i} ∣ + \frac{λ}{2} (f_{i} - u_{i})^{2})

where $λ$ is a positive parameter. The first term of this cost function is the total variation; the second term represents data fidelity. As $λ \to 0$ , the total variation term dominates, forcing the solution to have smaller total variation, at the expense of looking less like the input data.

This code is an implementation of the algorithm proposed by Chambolle in ^[1] to solve the ROF problem.

Parameters

image : ndarray: Input image to be denoised. If its dtype is not float, it gets converted with img_as_float.
weight : float, optional: Denoising weight. It is equal to $\frac{1}{λ}$ . Therefore, the greater the weight, the more denoising (at the expense of fidelity to image).
eps : float, optional: Tolerance $ε > 0$ for the stop criterion (compares to absolute value of relative difference of the cost function $E$ ): The algorithm stops when $∣ E_{n - 1} - E_{n} ∣ < ε * E_{0}$ .
max_num_iter : int, optional: Maximal number of iterations used for the optimization.
channel_axis : int or None, optional: If None, the image is assumed to be grayscale (single-channel). Otherwise, this parameter indicates which axis of the array corresponds to channels.
versionadded 0.19
channel_axis was added in 0.19.

Returns

u : ndarray: Denoised image.

Notes

Make sure to set the channel_axis parameter appropriately for color images.

The principle of total variation denoising is explained in ^[2]. It is about minimizing the total variation of an image, which can be roughly described as the integral of the norm of the image gradient. Total variation denoising tends to produce cartoon-like images, that is, piecewise-constant images.

Examples

2D example on astronaut image:

from skimage import color, data
img = color.rgb2gray(data.astronaut())[:50, :50]
rng = np.random.default_rng()
img += 0.5 * img.std() * rng.standard_normal(img.shape)
denoised_img = denoise_tv_chambolle(img, weight=60)

✓

3D example on synthetic data:

x, y, z = np.ogrid[0:20, 0:20, 0:20]
mask = (x - 22)**2 + (y - 20)**2 + (z - 17)**2 < 8**2
mask = mask.astype(float)
rng = np.random.default_rng()
mask += 0.2 * rng.standard_normal(mask.shape)
res = denoise_tv_chambolle(mask, weight=100)

✓

Aliases

skimage.restoration.denoise_tv_chambolle

Signature

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

Aliases