Objective

2

Texture is a repetitive pattern with high pixel values. Many natural images and works of art include textures such as cross-stitch and mosaic. In many cases

the visual system of individuals ignores the texture pattern and focuses on the main structure of an image. Texture filtering is a basic tool in the computer graphics and image processing fields; the goal of which is to suppress unnecessary texture details and maintain the salient structure in the image. In recent years

various texture filtering methods

which are mainly divided into global-and local-based filtering methods

have been proposed. Most of the existing texture filtering methods handle the small gradient texture images. However

handling the strong gradient texture and losing part of the structure is difficult. To solve this problem

we propose a texture filtering method by using texture gradient suppression and

$${L_0}$$

gradient minimization to suppress texture and maintain the structure.

Method

2

The main idea of this algorithm is to obtain an input image with strong gradient texture suppression and then attain the smooth filtering results through the traditional texture filtering method

which uses

$${L_0}$$

gradient minimization. Our method involves three steps to achieve the goal of image filtering. First

we improve the interval gradient operator

which has the capability to distinguish texture and structure pixels. We propose a directional interval gradient operator to increase the gradient amplitude by finding the main direction of the structure. We use a local contrast stretching strategy when calculating the direction interval gradient to improve the recognition capability of the weak gradient structure because the pixel gradient value of the weak structure area becomes smaller than the gradient value of the strong gradient texture. The directional interval gradient affects the texture suppression; thus

selecting a computational scale is particularly important. A scale adaptive strategy

which automatically selects the optimal scale for calculating interval gradient

is proposed. Second

we aim to obtain an input image with texture gradient suppression. In the first step

we obtain the directional interval gradient value

where the structured pixel is larger than the texture pixel. Then

a normalized directional interval gradient amplitude is used as the basis for attenuating the gradient of the original image. Image reconstruction is performed after image gradient suppression to obtain a texture-suppressed image with a gray pixel gradient that is smaller than the structural pixel gradient. In the image reconstruction step

we transform the reconstruction problem into the function optimization problem

and the fast Fourier transform is applied to the frequency domain to solve the problem. Finally

we use the

$${L_0}$$

gradient minimization algorithm with gradient lifting effect to filter the reconstructed image to remove the texture while preserving the structure because the texture gradient suppression operation causes a certain attenuation of the gradient of the structural pixels and thus results in the loss of the structure.

Result

2

We tested different types of pictures

including mosaics

nature

and grasslands

to prove the validity of the proposed method. The experiments are run on the windows platform

and the algorithm is implemented in MATLAB. Three main parameters are set

including the scale of calculating the directional interval gradient

the gradient weight

$$\lambda $$

in the image reconstruction step

and the smooth parameter

$$\lambda $$

in the

$${L_0}$$

gradient minimization.

$$\lambda $$

controls the suppression degree of the strong gradient texture in the reconstructed image. The texture is suppressed better with the increase in

$$\lambda $$

. We compare this algorithm against other texture filtering methods

including

$${L_0}$$

gradient minimization

rolling guidance filtering

interval gradient

co-occurrence filter

and relative total variation method. All methods use the code provided by the author and debug the optimal parameters to obtain the filter result. The field of texture filtering has no reasonable objective evaluation index. Therefore

the subjective evaluation of human eyes is used to compare the effects of different methods. The experimental results can be summarized as follows. In the mosaic image with strong gradient texture information and intractable tiny structures

this algorithm surpasses the effects of other algorithms in a strong gradient texture suppression

and the small gradient structure is also maintained. Our algorithm demonstrates superior image smoothing results in filtering out various scale textures and preserving small gradient structures when processing natural images. Moreover

texture filtering is applied to an image edge detection and detail enhancement

which achieves a favorable effect.

Conclusion

2

A texture filtering algorithm that combines texture gradient suppression and

$${L_0}$$

gradient minimization is proposed as a trade-off between strong gradient texture suppression and structure preservation in current texture filtering methods. This paper main purpose is to suppress the texture gradient of the input image. Thus

the texture and structure pixels obtain different texture filtering operations. The experiments demonstrate that our algorithm can maintain the main structure of the image and achieve smooth gradients. In the field of image recognition

image fusion

and edge detection that are susceptible to strong gradient textures

texture filtering has a significant potential for application.