A Residual Based Adaptive Image Sharpening Scheme

doi:10.21203/rs.3.rs-1760166/v1

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A Residual Based Adaptive Image Sharpening Scheme

https://doi.org/10.21203/rs.3.rs-1760166/v1

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The sharpening is a scheme applied to highlight the intensity transitions in an image. This enhancement increases edge acutance and significantly improves the overall sharpness of processed images. Image sharpening is of enormous importance in medicine for diagnosis. Noise overshoot and over-sharpening effects occur in classical sharpening algorithms. The adaptive approach skips the noise producing a better sharpening scheme. Abrupt pixel value changes, if adequately emphasized, can be utilized effectively in the sharpening process. Since the residual image contains noise and edges, the bigger the filter size the greater the number of edges left in the residual image. Two residual images are produced first with different filter sizes. There is a relationship between these two residuals. A simple regression and standard deviation (±σ) is measured using these residuals. This linear equation is an expectation and the standard deviation is the difference between two residuals. One deviation (±σ) is proposed as the threshold. The points contained edges if the residual value is measured using a larger sized filter off ± σ than those residual using a smaller sized filter. A sensitive filter is adaptively applied to the image on those locations. It has been demonstrated that the proposed approach yields better results than the global filter as well as previous work on the P calculation results. A sharpening scheme without latent image noise amplification is useful for pattern recognition and machine-learning. In the future this scheme will be used to pre-process image segmentation.

Image sharpening

Residual

Nimble filter

Noise adaptive

Pratt FOM

Human awareness is extremely sensitive to the variations in the details and edges of an image. The blur effect is one of the most frequent degradations that occur in digital images. Blur reduces the visual quality of an image, making it difficult to perceive the important details properly.¹

Image sharpening is an enhancement helps increase edge acutance and significantly improves the overall sharpness of processed images.² Sharpness denotes any improvement technique that enhances the visual quality of edges and details in an image. Radiographic images have been widely processed with some degree of sharpness implemented.³

Digital images in medical applications can help doctors provide faster and more efficient diagnoses to patients. The quality of medical images directly influences the consequences of diagnosis. Nevertheless, in the acquisition process, medical images present degradations such as poor details or low contrast from time to time.⁴ In order to have better visual quality and/or acquire more medical information in images, sharpening is applied to highlight the intensity transitions in an image.²

Zohair recently developed a new filter to improve the sharpness of Mammograms, CT and MR medical images with good performance.¹ Mil´an et al. evaluated the sharpness and quality in coronary CT angiography (CCTA) datasets. They claimed that image sharpness is an important index in CCTA for the assessment of coronary artery disease (CAD).⁵ For the dental radiology, including the maxillofacial region, image sharpening is of enormous importance in diagnosis.⁶ Image sharpening applied to different types of dental radiology images will significantly improve the level of diagnosis and appropriate treatment. However, image sharpening significantly increases overshoot artifacts that adversely affect radiographic misdiagnosis and, as a consequence, could result in improper treatment.^{3, 6}

Many techniques have been proposed for image de-blurring or sharpening for enhanced image quality. Algorithms like unsharp masking (UM)⁷ and Laplace filtering, whose details can be found in report,⁸ have been proposed for spatial domain usage. The same effect can be achieved by adding the high frequency components to the original input signal.⁷ In addition, for frequency domain, techniques like Fourier series and wavelets have gained a lot of popularity due to their better results.^{9, 10} Edge detail improvement in an image is a process of extracting high frequency information from the image and then adding this details to the blurred image.¹¹

The UM applied to different types of radiological images, will significantly improve the level of diagnosis and appropriate treatment.⁶ This manipulation may in fact degrade the image quality by introducing artifacts such as overshoot that can lead to misdiagnosis. Clark et al. suggested that all digital dental images should be processed with some degree of UM.³ While UM sometimes improves radiographic quality but the production of an overshoot artifact from UM can adversely influence diagnosis in detecting dental caries. The fit between a finish line and a restoration margin is sometimes inaccurate. Increased awareness of diagnostic errors from overshoot artifacts will improve diagnostic acuity and result in better patient care and oral health outcomes.³ Nevertheless, image sharpening is presence of various challenges, including noise amplification, and over-sharpening effects.^{2, 8, 12}

To decrease the overshoot image noise, adaptive UM and nonlinear modules were proposed.^{2, 7, 9, 10} These algorithms sharpen images effectively and do not amplify the noise concurrently. Hence, the development of such adaptive nonlinear modules for image enhancement may be a better choice.² Lin and Chen² recently suggested a novel adaptive image sharpening scheme. In their work a norm map was produced by measuring the first-order gradient in an image. These gradient norms, sorted and accumulated, can obtain a CDF (cumulated distribution function). Taking the second derivative of this CDF and then finding the point equal to 0 locates the inflection point. The inflection point of this CDF curve is used as a threshold to distinguish edges or not. A simple sharpness filter, named nimble filter, is applied to the locations in the image where the gradient norm is greater than T to adaptively determine sharpness.^{1, 2}

The uncorrelated part from an image is extracted for de-noising a residual image (RESI). Each pixel grey-level in the image is assumed a combination of signal and noise parts. The subtraction between two correlated pixels should yield only the uncorrelated part which is considered to be noise. A residual image is defined as the value of the subtraction between an original image and its smoothed version. The subtraction can effectively remove the signal part and leave the noise part.¹³

Many RESI based state-of-the-art de-noise algorithms were proposed in past decades. Baloch et al. developed a RESI correlation regularization de-noising scheme that minimizes the correlation between neighboring RESI patches.¹⁴ Roychowdhury et al. estimated noise in chest CT image data with varying image quality using RESI.¹⁵ To estimate white Gaussian noise in images, a work surveyed six methods and found that the noise estimation using the standard deviation measurement in RESI was most reliable.¹⁶

The RESI should possess the statistical properties of contaminating noise. Nevertheless, it is very likely that the residual patch contains remnants from the clean image patch.¹⁷ As a result, the RESI usually contains structures from the clean image patch; thus, it does not contain only contaminating noise. Brunet et al. applied a statistical test on the RESI and found that RESI did not contain only pure noise; as there were structures present.¹⁷ They de-noised RESI with an adaptive Wiener filter first and then parts of the cleaned RESI were added back into the de-noised original image. Their iterative scheme produced gains in both PSNR and SSIM image quality indices.

A RESI can be defined as RESI = ORGI − SMI using the subtraction value between an original (ORGI) image and its smoothed (SMI) version.

A nonlinear module, named the Moran statistics, was proved corresponds well with the variation in image spatial properties.^{18, 19} Some works applied these statistics to medical images to distinguish noise or edges and then adaptively processed the images. They showed that the RESI using a 5×5 window average filter had higher structural information than using a 3×3 window. This effect indicated that a bigger filter size resulted in more structural information in a RESI or more blurred in SMI. These works also showed that the RESI of a smaller window has more noise information than a big window. This is also consistent with general signal procession knowledge.^{20, 21}

The detection filter scale is also an important issue in edge detection. Small-scaled filters are sensitive to edge signals but also prone to noise, whereas large-scaled filters are robust to noise but could filter out fine details.¹² A sensitive filter manipulates only five pixels in procession when applied to the image.¹ This filter had been proved as a good sharpening filter in a work of adaptive image procession.²

In first-derivative-based edge detection, the gradient image should be the threshold to eliminate false edges produced by noise. With a single threshold “Th”, some false edges may appear if “Th” is too small and some true edges may be missed if “Th” is too large.¹⁴ The proper choice of threshold value is very important and not easy work.

We propose an adaptive image sharpening scheme inspired by the work of Zohair¹, Lin and Chen² and others^7–10 on image sharpening scheme development. Since the RESI contained not only noise but with edges. The bigger the filters size the more the edges are left in RESI. There is a relationship between two RESIs using different filter sizes. The simple linear regression was measured using these RESIs to produce a regression equation and deviation (±σ). We assumed that a point in image contained only noise if the differences of these two residual images are within one ± σ in the equal position. In addition, the effects of variant threshold values were tested.

In this work images are first added with noise using the Gaussian distribution and then smoothed using two filter sizes. The RESIs were obtained from the subtraction between an original image and its smoothed images. The RESI_n was obtained by averaging the four nearest neighboring pixels and RESI₃ was by an average filter with 3×3 window. The RESI₃ is an expansion that compares four nearest neighboring pixels. The variations in each RESI_n vs. RESI₃ position should be small if they are on a smooth region or this region contained only noise. To model the relationship between RESI_n vs. RESI₃ a simple linear regression analysis was applied. We can use RESI_n to predict RESI₃. The location belongs to the edge if the variation in RESI₃ vs. RESI_n is off more than a value (i.e. one standard deviation ± σ). This pixel will be processed using a nimble sharpening filter. Those positions that belong to noise (RESI₃ < ±σ) are skipped. Measurements show that the similarity of adaptive sharpening is better than the global scheme and previous works compared using Pratt’s Figure of Merit (P).^{22, 23, 24}

The proposed method will be further developed and applied to improve image acuity, de-noising and image quality improvement. This method can be used to sharpen images with good noise reduction performance and de-noising with edge-preservation in the future.

ORI was used to represent the original image with noise. Pixel values in this image can be denoted as ORI(x,y). Images used in this study include traditional test image Lena, a synthetic image (a circle-phantom), and six medical images. Gaussian noise was priori added to these images before procession. Images were then filtered using a 3×3 average filter to make smoothed versions (SMI₃). Two residual images were produced concurrently, SMI_n was by averaging the four nearest neighboring pixels and SMI₃ using an average filter with 3×3 window.

2.1The difference between residual images ( RESI )

The RESI_n can be defined as RESI_n = ORI – SMI_n using the subtraction value between an ORI image and its smoothed version (SMI_n). In the same manner, the RESI₃ can be defined as RESI₃ = ORI – SMI₃ using the subtraction value between an ORI image and its smoothed version (SMI₃). The SMI_n is produced using an average of the nearest neighbor pixels and SMI₃ using a 3×3 window, respectively. As shown in Eqs. (1) and (2)

$${RESI}_{n}\left(x,y\right)=ORI\left(x,y\right)-\left(\frac{ORI\left(x+1,y\right)+ORI\left(x-1,y\right)+ORI\left(x,y+1\right)+ORI(x,y-1)}{4}\right)$$

$${RESI}_{3}\left(x,y\right)=ORI\left(x,y\right)-(\frac{1}{9}\sum _{j=-1}^{j=1}\sum _{i=-1}^{i=1}ORI\left(x+i,y+j\right)$$

It is obvious that the RESI₃ measurements were taken using a larger sized filter than RESI_n, as noted below (a 3×3 window, n = pixels of nearest neighbor, F(x,y) = center pixel). The assumption is that the RESI_n should approach RESI₃ if there is only noise in this area. However, if the RESI₃ deviated too much to RESI_n which means there is an edge in these areas.

	n
n	F(x,y)	n
	n

2.2The simple linear regression

Linear regression is a linear approach for modeling the relationship between a scalar response and one explanatory variable. The case of one explanatory variable is called simple linear regression.²⁵ In this regression, the observations are assumed to be the result of random deviations from an underlying relationship between a dependent variable (y) and an independent variable (x). A regression equation can be obtained such as y = ax + b (x = RESI_n, y = RESI₃). Figure 1 shows a linear regression map of Lena, the solid line shows the regression equation (y = 0.85x + 0.55), the dashed line shows one standard deviation from the regression line (standard deviation = σ = 3.17). This Lena image was added with noise prior to processing (µ = 0, deviation (DEV) = 20 and padded randomly on 20% of the entire image). We measured a RESI_n in each pixel corresponding to an RESI₃. The assumption is that if only noise exists in the 3×3 window the differences between RESI_n and RESI₃ should small (i.e. < ±σ). For each position, a corresponding RESI₃ can be examined using the regression equation and there is a probability of 68% for one standard deviation the RESI₃ will close to regression line. The RESI₃ higher than one standard deviation from regression line will be deemed that the 3×3 window has only noise and a probability of 32% contained edges. Following this, sharpening filter will apply in this position and skip those RESI₃ positions lower than one standard deviation. The one standard deviation$\pm$σ was used as a threshold to distinguish edges or not (or noise or not). In the beginning, the one$\pm$σ was selected for determining if the pixel contained an edge or not. This work will examine the results of various thresholds substituted a $\pm$σ.

2.3 Images

A Lena image and a synthetic image were used first in this study. Gaussian noise was priori added to this image before processing into medical images. Synthetic images with various pixel levels were made to verify the proposal. The image sizes are 512×512 and 10 bits in depth, as shown in Fig. 1(a). The outside background gray levels were 37 and inner 100. Sixteen circles with different gray levels from 300 (upper left) to 783 (bottom right).

Six common radiological images were used in this study: a CT body and an abdominal images (tomographic x-ray image), a chest image from Computed Radiography (CR), a mammographic image (MM, projected x-ray image), a MR head and a Knee images (tomographic intensity image). The CT data were 512 ⋅ 512 image size. The CR image was 440⋅440 image size, MM image 1024⋅1024 image size. The MR image was 512⋅512 image size, all medical images are 12 bits deep. These images were downloaded on the web.²⁶ Fig. 3 showed these images.

2.2 A Sharpness Filter

A new filter was recently proposed to improve the sharpness of medical images utilizing specific spatial image information with a distinct tuning weight, named nimble filter. ^{1, 2} This filter is described as below:

$NIM\left(x,y\right)=\left(\alpha \times SMI\left(x,y\right)\right)+\left(\left(1-\alpha \right)\times \left[\frac{SMI\left(x+1,y\right)+SMI\left(x-1,y\right)+SMI\left(x,y+1\right)+SMI(x,y-1)}{4}\right]\right)$ (3).

Where NIM(x,y) is the resulting image; x, y are spatial coordinates, SMI(x, y) is the smoothed image, $\alpha$ is a tuning weight that controls the amount of produced sharpness. It should fulfill ($\alpha$ >1), where higher values lead to shaper results.¹

2.3 Figure of Merit P

An empirical measurement proposed by Pratt for two binary images comparison objectively.²⁴ This figure of merit is one of the most commonly used to evaluate the performance quantitatively. Given scaling factor c (c = 1/9 as in Pratt’s work), and separation distance of d, P can be calculated as follows:^{2, 9, 22, 23, 24}

$$\text{P}=\frac{1}{{\text{B}}_{\text{N}}}\sum _{\text{i}=1}^{{\text{B}}_{\text{A}}}\frac{1}{1+\text{c}\times {\text{d}}^{2}\left(\text{i}\right)}$$

where B_N = max{B_I, B_A}, B_I and B_A are the ideal and actual edges in maps, respectively. The d(i) denotes the distance from the ith actual edge to the corresponding ideal edge. A higher P value indicates the similarity between the ideal edge map and the actual map. The greater the P is the better the detection results.

Images were processed through the proposed sharpening approach followed by an edge map calculation using Canny‘s approach.²² Edge maps are then measured quantitatively in terms of P. The original noise free image was treated as an ideal map and the processed images were set as actual maps.

Gaussian noise was added to a circle-phantom and Lena first respectively (for synthetic images, µ = 0, DEV = 50 and padded randomly 75% in the entire image, for Lena µ = 0, DEV = 20 and padded randomly 20% in the entire image,). Both images were smoothed using a 3×3 window average filter and a nearest neighbor separately. Concurrently, both RESI_n and RESI₃ were made using Eqs. (1) and (2) respectively.

A regression equation can be fitted using the least squares approach such as y = ax + b (x = RESI_n, y = RESI₃). The regression equation of circle-phantom the equation is y = 0.82x + 0.55 and σ = 15.19 for Lena is y = 0.85x + 0.55 and σ = 3.17. Images were then sharpened using both a nimble filter with a turning weight α = 6 globally and processed adaptively by this proposed scheme (a nimble filter with turning weight α = 6, and those points were skipped and thought as noise if they satisfy the equation RESI₃≦(ax + b)$\pm$σ. The circle-phantom profiles are shown in Fig. 2, (a) original phantom, (b),(c),(d) are profiles of upper line,(e),(f),(g) are profiles of the lower line. In this figure, the (b) and (e) are profiles of SMI₃, the (c) and (f) are profiles of a nimble filter with turning weight α = 6 processed globally, the (d) and (g) processed adaptively by proposed scheme. It is obviously that, the global scheme sharpening the edges simultaneously with the noise enlargement. In contrast, the adaptive method sharpened the edge without overshoot noise.

For Lena, the image edge maps were measured using Canny‘s approach. These edge maps were then measured quantitatively using P. The original image (without noise added) was treated as an ideal edge map and the processed images were set as actual edge map. The P measurements are 0.74 corresponding to global sharpening and 0.81 corresponding to proposed scheme sharpening adaptively, individually. A higher P value indicates the similarity between the ideal edge map and the actual edge map.

3.2 Application results on various medical images

Six medical images were chosen in this work. Most image processing systems suffer from noise from the original images. Therefore, we also tested the performance of the proposed algorithm in noisy conditions. All images were added with Gaussian noise at different noise levels. The mean (µ), standard deviation (DEV) and percentages (%) of noise padded in the whole image are shown in Table I.

Following, these images were smoothed using a 3×3 window average filter and a nearest neighbor individually. Both RESI_n and RESI₃ were made using Eqs. (1) and (2) respectively. A linear regression equation can be fitted using the least squares approach based on RESI_n, and RESI₃. The coefficients of linear regression equation, $\pm$σoff equation line, and percentage of sharpening for six medical images are briefly in Table II.

The slops (i.e. a) of linear regression equation are all around 0.85, and the intercepts (i.e. b) are all around 0.5, as noted in Table II. The head CT and MR T2 got higher standard deviations off linear equation (σ) caused by added Gaussian noise with high variances (for head CT µ = 0, DEV = 50, for MR T2 µ = 0, DEV = 40).

The performances of proposed scheme were showed in Table III. It is obvious that the adaptive sharpening have higher P values. The adaptive scheme shows better P results than the global using nimble filter.

4.1 Comparison with an adaptive scheme

Lin and Chen suggested a novel adaptive image sharpening scheme, recently.² In their paper, they measured first-order gradient norm in image then sorted and accumulated this gradient norm then made a CDF. Taking the second derivative of this CDF and then located the inflection point. The inflection point was used as a threshold to distinguishing edges or not. Following, a simple nimble filter was applied to the image if this gradient norm is greater than the threshold. This design skipped those positions where the gradient norm is lower than the threshold to achieve a sharpening adaptively.^{1, 2}

A CT and a MRT1 cases were select to made comparisons. The CT was free of noise added according to previous work. The P of this work is better than previous work (0.88 vs. 0.83) on same turning weight, as noted in Table IV. Table V showed the results of P for a MRT1 image. This image was pre-added Gaussian noise (µ = 80, DEV = 9).² The P of this work is lower than previous work on same turning weight (0.86 vs. 0.89), as showed in Table V. However, the P value was increased and equal to the previous work (0.89 vs. 0.89) when we modified the threshold from $\pm$σto$\pm$σ/2. Originally, the RESI₃ out of one $\pm$σ from regression line will be deemed that the 3×3 window not only noise and a probability of 32% positions contained edges. In this case, the $\pm$σ/2 mean that it is about a probability of 62% positions contained edges.²⁷ So there are more points will be processed as edges when we decreased the threshold.

4.2 The variations in σ impact on P

The inflection point was used as a threshold to distinguishing edges in the previous work.² This inflection point is one point only. In this paper, we proposed using the RESI₃ out of one $\pm$σ from linear equation of regression line will be deemed that the 3×3 window contained edges. However, what is the effect if we variant the threshold value, like$\pm$σ/2, $\pm$1.5σ,$\pm$ 2σ, or even $\pm$2.5σ. These correspond to the probability (σ/2 =62%, 1.5σ = 15%, 2σ = 5%, or even 2.5σ = 1.5%)²⁷ positions contained edges.

Three medical images were selected for testing; CR, CT and MRT2. Table VI shows P for variations of ± σ and the percentage of calculation in image (i.e. %). The P of CR increases with a higher ± σ and decreases the image calculation. However, the P trend is smooth. The highest P point of CT is around ± σ. The P of MR increases with higher the ± σ and the highest point around ± 2σ. This testing illustrated that varied the ± σ can optimize the result.

This report proposed an efficient adaptive image sharpening scheme that is capable of performing in noisy conditions. Since the residual image contained noise with edges, the bigger the filters size, the greater the number of edges left in the residual image. The linear regression was measured using these residual images to produce a regression equation and deviation (±σ). We assumed that a point in the image contained only noise if the differences between two residual images within one ± σ in the equal position. The proposed approach was priori examined using synthetic image and Lena. This examination demonstrated to yield better results than the global nimble filter based on the P calculation.

This scheme was applied to six medical images and had good performance. A previous paper suggested using the inflection point as a threshold to distinguish edges or not. The proposed approach has been demonstrated to yield better results than the global nimble filter and classical UM approach.² Nevertheless, the inflection point is one point only. This novel proposed scheme of adaptive sharpening can have many thresholds when the ± σ rates vary and made better results compared to the work of Lin and Chen.²

This sharpening image scheme has less latent noise amplification is useful for pattern recognition and machine-learning. In the future this scheme will be used to pre-process image segmentation.

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All data generated or analyzed during this study are by ourselves or included in this web:

https://barre.dev/medical/samples/#introduction.

Competing interests:

The authors declared that they have no competing interests.

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Authors' contributions:

Rong-Hui Lu and Tzong-Jer Chen wrote together the main manuscript text and Tzong-Jer Chen made edit. Rong-Hui Lu prepared figures and tables. All authors reviewed the manuscript.

Acknowledgments:

This work was supported in part by Education and Scientific Research Grants for Young and Middle-aged Teacher, Fujian Province, China. (JAT190780).

Authors' information (optional):

Rong-Hui Lu, Information Technology and Laboratory Management Center, Wuyi University, Wuyishan, Fujian, 354300 China.

Tzong-Jer Chen*, Department of Mathematics & Computer Science, Wuyi University, Wuyishan, Fujian, 354300 China.

*Corresponding author: Tzong-Jer Chen, Ph.D., Associate Professor

Phone: +86-1809-4158256

E-mail: [email protected]

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Table I to VI are available in the Supplementary Files section.

No competing interests reported.

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A Residual Based Adaptive Image Sharpening Scheme

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Abstract

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1. Introduction

2. Methods And Materials

2.3 Images

2.2 A Sharpness Filter

3. Experiments And Results

3.2 Application results on various medical images

4. Discussions

4.1 Comparison with an adaptive scheme

4.2 The variations in σ impact on P

5. Conclusion

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References

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Supplementary Files

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