Joonpyo Park

Jong Ho Kim
email: kimjongho@rist.re.kr

Myoung Gyun Kim

Young Joon Lee

Tingu Li

Kwang Seok Lee

Jong Sup Lee

Continuous Casting of Aluminum and Copper Clad Ingots under Electromagnetic Fields

Keywords: continuous casting, aluminum, cooper, clad ingot, electromagnetic stirring

Aluminum and copper clad ingots have gained great attention because its versatility to wide application areas, such as brazing sheet, light weight electrical wire and clad plate. In general, clad sheet and wire can be fabricated by rolling bonding or adhesive bonding. However these processes require complicated pre-treatment and processing and its processing cost is high. In this study, casting of aluminum and copper clad ingot was suggested and integrated by modification of direct chill casting and horizontal casting. Key parameter for successful interface bonding was precise control of cooling rate in the mould divider. To improve the bonding behavior and microstructure of clad ingot, electromagnetic stirring was applied during continuous casting process. By applying electromagnetic stirring, the interface bonding of clad ingot was improved with refined microstructure. In result, uniform and strongly bonded aluminum and copper clad ingot was fabricated under electromagnetic field. Finally preliminary study of rolling and extrusion of clad ingots were conducted and it shows promising results for fabrication of clad sheets and wire.

Introduction

It is desirable for many purposes to fabricate aluminum and copper sheets made of two or more alloy layers. There are large potential markets for clad products consisting of two or more layers of different alloys. Such products are used to produce clad sheets and wire for various applications such as brazing sheet, aircraft plate where two or more combined properties is required. In the manufacture of those products, a large portion is produced by methods employing roll cladding or bonding. It is reliable process but has a disadvantage in the interface between the layers which is not metallurgically clean and bonding of the layers can often be a problem. An alternative approach of fabricating clad products is a novel and inexpensive method of casting composite metal bodies suitable for further processing by conventional metal working methods. Conventional aluminum and copper alloy ingots have been cast by continuous casting process known as direct chill (DC) casting. In this process, molten metal has been poured into the top of open ended mould. Such a system is commonly used to produce monolithic ingots for rolled and extruded products. There has been an interest in casting layered ingots to produce a clad ingot from 1950s. This has typically been carried out using modified direct chill casting of simultaneous or sequential solidification of two alloys. In Robinson's patent, a casting system is suggested where an internal partition is placed within the mould cavity to substantially separate areas of different alloy compositions. In Binczewski's patent, a method is suggested for producing a composite ingot by DC casting where an outer layer of higher solidus temperature is cast about an inner layer with a lower solidus temperature. Recently Mark Douglas Anderson from Novelis Inc. has integrated clad ingot casting technology so called Fusion Technology as a commercial scale successfully. This study includes a method and apparatus for direct chill casting two aluminum and copper layers at one time to form a composite ingot with electromagnetic stirring technique. For a good adhesion between the two layers, it is desirable to ensure that the layers, while being cast together in a single mould, are formed sequentially so that molten metal of one layer contacts previously cast semi solid metal of another layer. The appropriate control of interface cooling may also prevent harmful oxide formation at the interface between the metal layers, again improving mutual adhesion of the layers. Clad ingots were subjected to further specialized metal working such as hydrostatic extrusion and differential speed rolling. Finally it is confirmed that clad wire and sheets were successfully fabricated from aluminum and copper clad ingots.

Experimental Method

Casting experiments were performed using and AA1050, AA6061 and pure Cu alloy. A part of the raw AA6061 alloy was modified with 400 ppm Ti by adding AlTiB1 during ingot preparation. The experimental setup is schematically depicted in Fig. 1. The copper mould with slit and AA1050 and AA6061 were used in vertical slab casting. The vertical casting machine was equipped with direct cooling water spray into mould and billet. The mould has same structure of monolithic casting however divider was installed inside mould. The divider has water and air cooling auxiliary parts to control the solidification behaviour of the interface between two layers. The graphite mould and AA1050 and pure copper were used in horizontal billet casting machine. Indirect cooling was applied to horizontal casting machine. Casting speed was varied up to 150 mm/min and 1500mm length billet and slab were fabricated with two casting machines. The rotating magnetic field equipment was installed around mould and low frequency magnetic field was applied to generate the melt rotation. The cast samples were cut and polished to reveal the microstructure. The microstructure was observed with low magnification camera and optical microscope. The grain size, interface microstructure and adhesion properties were estimated to find the effect of melt stirring. Finally slab was cut into designated size for rolling. In case of two layered aluminium slab, differential speed rolling was applied to get sound sheet sample. Rolling process was in done in 300 o C and differential speed ratio was 1.6. In case of aluminium and copper clad billet, hydrostatic extrusion process was applied to obtain enhanced clad wire.

Results and Discussion

The slab clad ingot casting is done successfully by adjusting processing parameters such as melt temperature, melt level, casting speed, and cooling water. In order to find optimal processing parameters, numerical simulation study was done and checked with several experiments. The most important parameter for slab clad ingot casting was the cooling of divider by cooling water and air. If the cooling water and air cools too much, the interface adhesion is poor and occasionally separated. If the cooling is not enough, two melt is mixed and layered structure was not obtained after casting. After establishment of sound casting condition, rotating magnetic field was applied to observe the effect of magnetic field. The solidification structures of slab clad ingot were shown in Fig. 2. AA6061 side shows refined grain size due to addition of grain refiner. However AA1050 side shows coarse and columnar structure in Fig. 2(a) and it is observed in typical aluminum casting sample. If rotating magnetic field was applied during casting, microstructure was changed as refined structure. The equiaxed area of EMS applied sample is around 72% of total area and its grain size is greatly reduced. The rotating magnetic field induces shear flow ahead at the dendrites. Also interface adhesion shows difference between two samples. Around edge region of interface, large shrinkage gap is found in Fig. 2(a) however no gap at edge interface was found in Fig. 2(b). The difference of melt temperature between center and edge region during casting process is large without EMS. The EMS induces melt stirring and uniform temperature was obtained. Therefore uniform solidification was happened along the interface. The adhesion properties were evaluated with tensile and bending test. Stress-strain curve for clad ingot sample shows good agreements with microstructure. Fig. 3: The tensile test of AA1050/AA6061 clad ingots and its stress-strain curve Fig. 3 shows the tensile test samples of AA1050/AA6061 samples and its stress-strain curve. As shown in Fig. 3, the failure is occurred at the AA1050 side, which means the strength of interface is enough to endure the failure. Each sample of AA1050, AA6010 monolithic and AA1050/6061 clad was tested and its stress-strain curve were compared. Two monolithic samples show typical values of yield strength and elongation. Clad sample shows low yield strength and elongation but these values are not directly related to clad sheets. The tensile test along sheet rolling direction shows mid values of two monolithic materials. It was possible to fabricate different aluminum alloy combination with adjusting casting conditions. AA1050/AA2024, AA4004/AA5052 were fabricated with same casting machine. Clad billet casting was done with horizontal casting machine. Out region is cooper and inner region is aluminum as shown in Fig. 4. The melt temperature of aluminum was main parameters to obtain clad sample. Low melt temperature of aluminum induces fast solidification before filling the hollow copper but high melt temperature generates re-melting of copper outer billet. Precise control of melt temperature was needed to obtain fully filled clad billet. Also casting speed, cooling water intensity and cooling water temperature were important factors to determine billet casting process. Fig. 4(b) shows good interface bonding due to processing parameter control and EMS application. In horizontal casting of clad billet, bottom interface shows good adhesion but top interface shows shrinkage gap with EMS. If EMS is applied during casting, aluminum melts circulated the inner region and fills uniformly. Casting defects at interface region still exist but it can be removed by severe plastic deformation such as extrusion. However large defects of non-EMS samples exhibits as large crack or process instability during plastic deformation. It also shows grain refinement effect aluminum alloy by applying EMS. It was also possible to fabricate clad billet of AA3003/AA4004 alloy combinations with vertical casting machine. Clad slab was rolled and the results were shown in Fig. 4. The significant difference of flow stress between AA1050 and AA6061 induces bending of rolled sheet. The thickness ratio of AA1050/AA6061 was changed to suppress the bending behavior. Differential speed rolling was also applied as same purpose. Clad sheet was successfully fabricated by optimizing rolling condition and it shows no significant rolling defect. If more differential speed ration is applied, bending will be adjusted as normal condition. Al/Cu billet was extruded by hydrostatic extrusion method. Uniform stress distribution around billet eases the extrusion process even though each clad layer has different physical properties. The electrical properties were checked after extrusion and its values were comparable to monolithic copper wire.

Conclusion

This study demonstrates the clad ingot casting with vertical and horizontal casting machine. The impact of electromagnetic stirring on microstructure and interface adhesion was evaluated and forced convection influences significantly the macrostructure. Finally clad Al/Al slab was subjected to differential speed rolling and sound clad sheet was fabricated. Cu/Al billet was subjected to hydrostatic extrusion process and clad wire was fabricated successfully.

Fig. 1 :

 1 Fig. 1: Schematics of the vertical and horizontal continuous casting of clad ingot with electromagnetic stirrer

Fig. 2 :

 2 Fig. 2: The cross section images of AA1050/AA6061 clad ingots (a) without EMS, (b) with EMS

Fig. 4 :

 4 Fig. 4: The cross section images of Cu/Al clad ingots, (a) low melt temperature (b) optimum temperature and (c) high temperature with EMS applications

Fig. 4 :

 4 Fig. 4: The AA1050/AA6061 clad sheet from clad slab ingot and Cu/Al wire from clad billet

Acknowledgment

This study was supported by a grant from the R&D program for Core Technology of Materials funded by the Ministry of Trade, Industry and Energy, South Korea.


Bin Chen

Yang Chen

Zhuhong Shao

Tong Tong

Limin Luo

Blood vessel enhancement via multi-dictionary and sparse coding: Application to retinal vessel enhancing

Keywords: Blood vessel enhancement, Multi-dictionary, Sparse coding, Retinal vessel image

Blood vessel images can provide considerable information of many diseases, which are widely used by ophthalmologists for disease diagnosis and surgical planning. In this paper, we propose a novel method for the blood Vessel Enhancement via Multi-dictionary and Sparse Coding (VE-MSC). In the proposed method, two dictionaries are utilized to gain the vascular structures and details, including the Representation Dictionary (RD) generated from the original vascular images and the Enhancement Dictionary (ED) extracted from the corresponding label images. The sparse coding technology is utilized to represent the original target vessel image with RD. After that, the enhanced target vessel image can be reconstructed using the obtained sparse coefficients and ED. The proposed method has been evaluated for the retinal vessel enhancement on the DRIVE and STARE databases. Experimental results indicate that the proposed method can not only effectively improve the image contrast but also enhance the retinal vascular structures and details.

Introduction

The human body contains different types of blood vessels, which constitute a network of arteries and veins. The visualization of these blood vessels is important for disease diagnosis and improving the planning and navigation in interventional procedures [START_REF] Sofka | Retinal vessel centerline extraction using multiscale matched filters, confidence and edge measures[END_REF][START_REF] Ikram | Retinal vessel diameters and risk of Hypertension the rotterdam study[END_REF][START_REF] Mcgeechan | Meta-analysis: retinal vessel caliber and risk for coronary heart disease[END_REF][START_REF] Gegúndez-Arias | A function for quality evaluation of retinal vessel segmentations[END_REF]. For instance, retinal vessel images are widely used by ophthalmologists for the disease diagnosis such as diabetes, hypertension, cardiovascular disease and stroke. In case of changes in vessel caliber, branching angle or vessel tortuosity are results of hypertension [START_REF] Wong | Hypertensive re-tinopathy signs as risk indicators of cardiovascular morbidity and mortality[END_REF]. The onset of neovascularization is a sign of diabetic retinopathy, and a complication of diabetes which leads to the cause of blindness [START_REF] Sussman | Diagnosis of diabetic eye disease[END_REF]. However, due to the imperfect imaging condition, the quality of blood vessel images is usually poor, making it hard to recognize the vascular structure clearly.

An effective way to overcome these issues is to use the image enhancement technology. The main purpose of blood vessel enhancement is to highlight the vascular structures and details [START_REF] Akram | Blood vessel enhancement and segmentation using wavelet transform[END_REF][START_REF] Truc | Vessel enhancement filter using directional filter bank[END_REF][START_REF] Ricci | Retinal blood vessel segmentation using line operators and support vector classification[END_REF]. In this paper, we propose a novel method for the blood Vessel Enhancement via Multi-dictionary and Sparse Coding (VE-MSC). The DRIVE 1 and STARE 2 databases are used to evaluate the proposed method. Experimental results demonstrate that the image contrast is effectively improved and the retinal vessel structures and details are well enhanced. A comparison with state-of-the-art methods has also been carried out in the retinal vessel enhancement.

The rest of the paper is organized as follows. In Section 2, the related works about blood vessel enhancement are briefly reviewed. The proposed method VE-MSC and its application on r e t i n a l

Related works

According to different emphasis on the prior knowledge, blood vessel enhancement methods can be categorized into three groups: histogram based, transformation based and filter based.

(1) Histogram-based method [START_REF] Zuo | Range limited bi-histogram equalization for image contrast enhancement[END_REF][START_REF] Chen | A new image quality measure for assessment of histogram equalization-based contrast enhancement techniques[END_REF][START_REF] Celik | Two-dimensional histogram equalization and contrast enhancement[END_REF][START_REF] Stark | Adaptive image contrast enhancement using generalizations of histogram equalization[END_REF][START_REF] Zhang | Histogram partition based gamma correction for image contrast enhancement[END_REF] utilizes the prior information of blood vessel to equal the histogram distribution. For instance, histogram equalization (HE) [START_REF] Huang | Natural color image enhancement and evaluation algorithm based on human visual system[END_REF] and contrast limited adaptive histogram equalization (CLAHE) [START_REF] Reza | Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement[END_REF] are two basic methods used for the retinal vessel enhancement. However, some retinal vessel details are lost during the equalization. Kuldeep et al. [START_REF] Singh | Image enhancement using exposure based sub image histogram equalization[END_REF] proposed a contrast enhancement method based on the sub-image histogram equalization for low exposure gray scale image. The histogram was clipped using a threshold value as an average number of gray level occurrences to control the enhancement rate, but it was only used for the low exposure gray scale image.

(2) Transformation-based method transfers the image to other space [START_REF] Lee | Contrast enhancement using dominant brightness level analysis and adaptive intensity transformation for remote sensing images[END_REF][START_REF] Zhang | Color image enhancement based on HVS and PCNN[END_REF][START_REF] Agaian | Transform-based image enhancement algorithms with performance measure[END_REF][START_REF] Li | Automatic SAR image enhancement based on nonsubsampled contourlet transform and memetic algorithm[END_REF], where the blood vessel can be enhanced. Miao et al. [START_REF] Liao | Retinal vessel enhancement based on multi-scale top-hat transformation and histogram fitting stretching[END_REF] proposed a retinal vessel enhancement algorithm based on multi-scale top-hat transformation and histogram fitting stretching. However, part of the vascular structures were changed through the transformation and histogram stretching. In addition, some parameters utilized in the method were sensitive to the initialization. Li et al. [START_REF] Li | A novel method of image enhancement based on the fractional Fourier transform[END_REF] applied the fractional Fourier transformation to the image enhancement. However, it also suffered the blood vessel details lost problem during the selection of image features.

(3) Filter-based method utilizes a filter or multiple filters [START_REF] Rubel | Efficiency of texture image enhancement by DCT-based filtering[END_REF][START_REF] Seow | Ratio rule and homomorphic filter for enhancement of digital colour image[END_REF][START_REF] Paul | MR image enhancement using an extended neighborhood filter[END_REF][START_REF] Remaki | Numerical schemes of shock filter models for image enhancement and restoration[END_REF] to enhance the blood vessel.

Fraz et al. [START_REF] Fraz | An ensemble classification-based approach applied to retinal blood vessel segmentation[END_REF] proposed a retinal vessel enhancement method based on decision trees and

Gabor filter, while it also had the vascular details lost problem. To overcome these weaknesses, a medical image enhancement method using morphology-based homo-morphic filtering technique was developed by Oh et al. [START_REF] Oh | Feature enhancement of medical images using morphology-based homomorphic filter and differential evolution algorithm[END_REF]. However, the contrast of the blood vessel was low, and the vascular details lost problem was also existed.

The vascular details enhanced by these classical reported methods in literatures are hardly to be completely reserved, and the contrast of the enhanced vascular image is not high enough. To solve these problems, a novel blood vessel enhancement method using multi-dictionary and sparse coding is proposed in this paper. To the best of our knowledge, this is the first time to achieve the blood vessel enhancement via multi-dictionary and sparse coding. In order to gain the blood vascular structures and details, two corresponding dictionaries are generated. One is the representation dictionary (RD) generated from the blood vessel images, the other one is the enhancement dictionary (ED) extracted from the corresponding label images. The patches in RD and ED are selected through the information of the label images to optimize the multi-dictionary.

Then the input target image is represented by RD to get the sparse coefficients via a sparse coding process. Finally, the enhanced blood vessel image is obtained from the solved sparse coefficients and ED. The effect of dictionary patch size and dictionary patch selection are analyzed in the experiments.

Vessel Enhancement via Multi-dictionary and Sparse Coding (VE-MSC)

RD and ED generation

Dictionary based methods have been studied in medical image processing [START_REF] Elad | Image denoising via sparse and redundant representations over learned dictionaries[END_REF][START_REF] Shen | Lazy random walks for superpixel segmentation[END_REF][START_REF] Zhang | Binary PSO with mutation operator for feature selection using decision tree applied to spam detection[END_REF][START_REF] Chen | Curve-like structure extraction using minimal path propagation with back-tracing[END_REF], which differs in how they form the overcomplete dictionary. For instance, Chen et al. [START_REF] Chen | Artifact suppressed dictionary learning for low-dose CT image processing[END_REF] proposed a Low-Dose CT (LDCT) image processing method based on artifact suppressed dictionary learning, where an overcomplete global dictionary was included. Li et al. [START_REF] Li | An efficient dictionary learning algorithm and its application to 3-D medical image denoising[END_REF] used the group-sparse representation with dictionary learning for medical image denoising and fusion, and the dictionary utilized was also overcomplete. In the proposed method, both the generated RD and ED are overcomplete, which are then used for enhancing the blood vascular structures and details.

Each patch in RD has the unique and corresponding patch in ED, and they have the same location in the respective dictionary. RD is generated from the original blood vessel images, ED is extracted from the corresponding label images with value 0 or 1. Let f be a 2D gray image in a blood vessel image database. The image size of f is M M , and its sequence number in the blood vessel image database is k . Then a pixel with the location ( , )

x y in f can be remarked as ( , , ) f x y k . Let l f be the corresponding label image of f , which is the blood vessel segmentation result delineated manually by an expert. Then the corresponding label value of ( , , ) f x y k in the label image l f is denoted as ( , , ) l f x y k . A patch in RD ( RD p ) and its corresponding patch in ED ( ED p ) are defined as: the corresponding patches, they have the same location in the respective dictionary. Most patches in the dictionaries contain blood vessels due to the patch selection in Eq. ( 1). The impact of background is mostly eliminated through the ED, and the blood vascular structures and details can be mostly reserved by the two dictionaries.

RD = ED = : ( , , ), , 1,... : ( , , ), , 1,..
. h l h h l l h p f s s k h h h if f t p f s s k h h h if f t , (1)

Sparse coding and blood vessel enhancement

The multi-dictionary (RD and ED) is generated from Eq. ( 1 . Let o f be the original blood vessel image to be enhanced (a 2D gray image), and 0 f p is a patch extracted from 0 f . To get the sparse coefficients used in the blood vessel enhancement processing, 0 f p is represented as:

0 RD RD RD 1 1 2 2
...

f n n p p p p . (2)
Since the representation in Eq. ( 2) is sparse, most of the coefficient i will be zero, let

[ , ,... ] n , and the satisfy the restricted isometry property (RIP) [START_REF] Chartrand | Restricted isometry properties and nonconvex compressive sensing[END_REF][START_REF] Baraniuk | A simple proof of the restricted isometry property for random matrices[END_REF]. Then the sparse solution can be obtained by solving the following equation [START_REF] Tong | Segmentation of MR images via discriminative dictionary learning and sparse coding: Application to hippocampus labeling[END_REF]:

0 2 0 2 ˆsubject to RD f min p . ( 3
)
where the is an error target for the sparse solution ( n h h 2 , the Eq. ( 3) doesn't have a unique solution. However, when the solution of Eq. ( 3) is sparse enough, it can be solved efficiently by many sparse coding methods [START_REF] Wright | Robust face recognition via sparse representation[END_REF][START_REF] Ma | Visual tracking using strong classifier and structural local sparse descriptors[END_REF][START_REF] Figueiredo | Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems[END_REF]. In the proposed method, an efficient Batch Orthogonal Matching Pursuit (Batch-OMP) method [START_REF] Rubinstein | Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit[END_REF] is used for obtaining the sparse coding coefficients in Eq.

where e f is the enhanced blood vessel image made up of patches e f p , and the sparse coding coefficients in Eq. ( 4) is the same as in Eq. ( 3). As the values in ED are binary, the gray value of e f is usually small. Then we rescale e f to [0, 255] by the following equation:

where min e f is the minimum in e f , max( ) is an operator to find the maximum, and er f is the final enhanced image.

The algorithm steps of the proposed VE-MSC are given as follows:

1) Gain RD and ED a) Initial the , , , d h t L in Eq. ( 1) and in Eq. 2) Represent the target image 0 f with RD (Eq. ( 2));

3) Solve the sparse coding coefficients with Batch-OMP (Eq. ( 3)); 4) Construct the enhanced patch e f p using and ED (Eq. ( 4));

5) Get the enhanced image er f through a gray rescaling (Eq. ( 5)).

A detailed flow chart of the proposed method is shown in section 3.3 (application on retinal vessel enhancement). In general, the blood vessel image to be enhanced is not in the database used for the generation of RD and ED, but they are the same type of blood vessel images. For instance, we use the DRIVE to gain the dictionaries and the STARE to be the target image 0 f in the application of retinal vessel enhancement. the dictionary building process, most of the retinal vascular structures and details are obtained through a patch selection, which is introduced in Eq. ( 1). Then a representation to the target image o f is utilized to solve the sparse coefficients . After getting the dictionaries (in Eq. ( 1))

Retinal vessel enhancement via VE-MSC

and sparse coefficients (in Eq. ( 3)), we use the ED and sparse coefficients to obtain the enhanced retinal vessel image with Eq. ( 4). Finally, the enhanced retinal vessel image is rescaled by Eq.

(5).

Experiments and results

To In order to evaluate the enhancement quality quantificationally, two metrics [START_REF] Oh | Feature enhancement of medical images using morphology-based homomorphic filter and differential evolution algorithm[END_REF] are used:

(1) C represents the contrast between the retinal vessels and the background (retinal regions except the vessels), which is defined as:

Y G C Y G , ( 6
)
where Y is the average gray values of the retinal vessels, G is the average gray values of the background.

(2) CII represents the contrast rate between enhanced image ( en C ) and the original image ( or C ), which is defined as:

en or C CII C . ( 7
)
The larger the value of C is, the more obvious the difference between the retinal vessels and the background is. It should be mentioned that black background pixels outside the pupil are not calculated in our method. In the experiment, the proposed approach was compared with HE [START_REF] Huang | Natural color image enhancement and evaluation algorithm based on human visual system[END_REF], CLAHE [START_REF] Reza | Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement[END_REF], methods in [START_REF] Liao | Retinal vessel enhancement based on multi-scale top-hat transformation and histogram fitting stretching[END_REF][START_REF] Fraz | An ensemble classification-based approach applied to retinal blood vessel segmentation[END_REF][START_REF] Oh | Feature enhancement of medical images using morphology-based homomorphic filter and differential evolution algorithm[END_REF]. Meanwhile, the effects of dictionary patch size ( h ) and patch selection ( t ) were also provided.

Effect of dictionary patch size ( h )

The effect of using different patch size is analyzed in this section. Fig. 4 shows the C values of DRIVE testing set with different patch sizes. In order to optimize the dictionaries (RD and ED), we set the parameter t {5, 10, 14, 18, 25, 36}, respectively. It can be observed that the best overall performance on the image contrast is achieved when the patch size is set to 12×12. The patch size 9×9 has the worst overall performance on the image contrast in Fig. 4. This is because of the dictionary patch size is related to the retinal vascular local geometry, and it leads to an imperfect enhancement performance when the patch size isn't suitable for the retinal vascular width. However, the influence of the retinal vascular local geometry can be reduced to a minimum due to the dictionary patch selection and sparse coding.

Effect of dictionary patch selection ( t )

Besides the above experiments, the effect of dictionary patch selection ( t ) was also provided. decreased and the mean gray value of the enhanced retinal image is increased with the increase of t . The reason of these phenomena is the patches selection during the dictionary building.

When the t is increased, the extracted patches from Eq. ( 1) contain more retinal vessel pixels, so the average value of the ED is increased. Then the average gray value of the enhanced retinal vessel image is also increased, leading to a low contrast between the background and retinal vessel region.

Enhancement results

All the RD and ED used in the retinal vessel enhancement of two databases (DRIVE and STARE) were extracted from DRIVE database. We utilized the DRIVE testing set (image index

No. [START_REF] Sofka | Retinal vessel centerline extraction using multiscale matched filters, confidence and edge measures[END_REF][START_REF] Ikram | Retinal vessel diameters and risk of Hypertension the rotterdam study[END_REF][START_REF] Mcgeechan | Meta-analysis: retinal vessel caliber and risk for coronary heart disease[END_REF][START_REF] Gegúndez-Arias | A function for quality evaluation of retinal vessel segmentations[END_REF][START_REF] Wong | Hypertensive re-tinopathy signs as risk indicators of cardiovascular morbidity and mortality[END_REF][START_REF] Sussman | Diagnosis of diabetic eye disease[END_REF][START_REF] Akram | Blood vessel enhancement and segmentation using wavelet transform[END_REF][START_REF] Truc | Vessel enhancement filter using directional filter bank[END_REF][START_REF] Ricci | Retinal blood vessel segmentation using line operators and support vector classification[END_REF][START_REF] Zuo | Range limited bi-histogram equalization for image contrast enhancement[END_REF][START_REF] Chen | A new image quality measure for assessment of histogram equalization-based contrast enhancement techniques[END_REF][START_REF] Celik | Two-dimensional histogram equalization and contrast enhancement[END_REF][START_REF] Stark | Adaptive image contrast enhancement using generalizations of histogram equalization[END_REF][START_REF] Zhang | Histogram partition based gamma correction for image contrast enhancement[END_REF][START_REF] Huang | Natural color image enhancement and evaluation algorithm based on human visual system[END_REF][START_REF] Reza | Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement[END_REF][START_REF] Singh | Image enhancement using exposure based sub image histogram equalization[END_REF][START_REF] Lee | Contrast enhancement using dominant brightness level analysis and adaptive intensity transformation for remote sensing images[END_REF][START_REF] Zhang | Color image enhancement based on HVS and PCNN[END_REF][START_REF] Agaian | Transform-based image enhancement algorithms with performance measure[END_REF] and STARE as the evaluating data. Fig. 6 and Fig. 7 present some retinal vessel enhancement results by using different methods. It can be seen that the retinal vascular structures enhanced by the proposed method are clear and complete in Fig. 6, and the small retinal vessels are also enhanced efficiently. The C and CII in Fig. 7 are the corresponding values of Fig. 6.

Obviously, the proposed method has the largest C and CII values. (a)), the maximum difference value of CII between the proposed method and method in [START_REF] Liao | Retinal vessel enhancement based on multi-scale top-hat transformation and histogram fitting stretching[END_REF] Compared with HE [START_REF] Huang | Natural color image enhancement and evaluation algorithm based on human visual system[END_REF], CLAHE [START_REF] Reza | Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement[END_REF], method in [START_REF] Liao | Retinal vessel enhancement based on multi-scale top-hat transformation and histogram fitting stretching[END_REF][START_REF] Fraz | An ensemble classification-based approach applied to retinal blood vessel segmentation[END_REF][START_REF] Oh | Feature enhancement of medical images using morphology-based homomorphic filter and differential evolution algorithm[END_REF], the enhanced retinal vessels by the proposed method VE-MSC are much easier to recognize. Based on the above results, it can be concluded that the proposed method has a much better enhancement performance on image contrast, retinal vascular structures, and retinal vascular details. The superiority of our method is mainly contributed to the adoption of multi-dictionary and sparse coding.

Conclusion

A novel vessel enhancement method (VE-MSC) via multi-dictionary (RD and ED) and sparse coding has been proposed in this paper. We evaluated the proposed method for the retinal vessel enhancement on the DRIVE and STARE databases. Experimental results show that the VE-MSC not only can effectively improve the image contrast but also enhance the retinal vascular structures and details. In the proposed method, two corresponding overcomplete dictionaries (RD and ED) are developed via a patch selection. The RD is utilized to gain the sparse coefficients ( ), then the enhanced blood vessel image is reconstructed by and ED. The patch size ( h ) and patch selection threshold value ( t ) both affect the enhancement performance of the blood vessel image. Further work includes: (i) improving the enhancement performance with a larger database;

(ii) applying on 3D blood vessel enhancement problems; (iii) extending to other image enhancement problems.

Fig . 1 markedFig. 1 .

 11 Fig .1 marked

  [START_REF] Mcgeechan | Meta-analysis: retinal vessel caliber and risk for coronary heart disease[END_REF]. Then we reconstruct the enhanced patch e f p according to the corresponding relationship from RD to ED:

Fig. 2 Fig. 2 .Fig. 3 .

 223 Fig. 2 shows a normal retinal vessel image and a background diabetic retinopathy retinal

  evaluate the performance of the proposed method, a series of experiments are performed on the DRIVE and STARE databases. The DRIVE database consists of 40 color retinal images, which were captured by Canon CR5 nonmydriatic 3 Charge-Coupled-Device (CCD) cameras at 45º field of view (FOV). Among them, the first 20 images are served as the testing set (image index No.1-20) and the rest constitute the training set (image index No.21-40), the size of each retinal image is 565 584 pixels. The STARE database contains 20 color retinal images (image index No.1-20, only use the images with hand labels) with the size of 700 605 pixels, which were captured by a TopCon TRV-50 fundus camera at 35º FOV.

Fig. 4 .

 4 Fig. 4. Values of C with different patch sizes (DRIVE testing set)

Fig. 5 Fig. 5 .

 55 Fig. 5 shows the C values of DRIVE testing set with different patch selection threshold values

Fig. 6 .Fig. 7 .Fig. 8 .

 678 Fig.6. Enhanced results with HE[START_REF] Huang | Natural color image enhancement and evaluation algorithm based on human visual system[END_REF], CLAHE[START_REF] Reza | Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement[END_REF], methods in[START_REF] Fraz | An ensemble classification-based approach applied to retinal blood vessel segmentation[END_REF][START_REF] Oh | Feature enhancement of medical images using morphology-based homomorphic filter and differential evolution algorithm[END_REF][START_REF] Liao | Retinal vessel enhancement based on multi-scale top-hat transformation and histogram fitting stretching[END_REF] and proposed method, column (b) to (g) respectively.

  is

4 .

 4 7937 (image No.13), and the mean difference value of CII is 2.0842. For the STARE (Fig. 8(b)), the maximum difference value is 3.2480 (image No.4), and the mean difference value of CII is 0.9124.

[START_REF] Zuo | Range limited bi-histogram equalization for image contrast enhancement[END_REF] in our method), 0 -norm l denotes the number of nonzero coefficients, and is the sparse constraint of this equation. Since

Acknowledgments

This research was supported by the National Natural Science Foundation under grants (81370040).


Philippe Leclaire

Thomas Dupont

Raymond Panneton

Acoustics of porous materials with partially opened porosity

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