Evaluation of Interpolation Techniques for Enhanced Super Resolution in Bio-Medical Imaging
Abstract- In this paper we evaluate the performance of novel image interpolation method based on the amalgamation of bicubic interpolation and 2D interpolation filter with the conventional interpolation methods. A high resolution image is first obtained by performing bicubic interpolation on the input image. The super resolution image is then obtained by implementing column and row interpolation filtering on the bicubic interpolated image. The second algorithm preserves edge smoothness and refines the interpolated pixels to produce perceptually superior quality images. The proposed interpolation method produces the least mean square error as compare to the linear interpolation methods. The results demonstrate that our new interpolation algorithm significantly augments the quality and Peak Signal to Noise Ratio (PSNR) of the interpolated images over linear interpolation methods.
Keywords- Image Interpolation; Two dimensional filter; Linear; Super Resolution
Doctors incessantly seek ways to acquire superior high resolution digital X-ray images for diagnosis, by means of expensive and unremittingly advance medical imaging systems. Thus it becomes imperative to ascertain economical, precise, efficient and effective ways to obtain high resolution images by using the existing medical imaging system. Super resolution (SR) (or HR) image reconstruction is one of the most effervescent research area that employ signal processing methods to obtain HR image from one or more LR images -. Super Resolution is the process of generating a high-resolution image (HR) from one or more low-resolution images (LR). Super resolution image enlargement can be obtained by using Transform based methods or Interpolation based methods. Image interpolation methods estimate unknown pixels of a high-resolution image from the known pixels of a low-resolution image to produce a high-resolution image.
Super resolution imaging is applied to a variety of applications such as biomedical imaging, surveillance, satellite images, video processing, printing etc. A paradigm of application of super resolution in biomedical imaging is the enlargement of low resolution digital X-ray images of patients by using super resolution algorithms. It is much easier for the doctors, clinicians and researchers to perform diagnosis by using enhanced super resolution X-ray images. Digital X-ray imaging of hard tissues such as skull, knee, femur, tibia, etc of patients is often required to analyze morphology and amount of fracture. It also shows anatomical features of hard tissue and assists early diagnosis of bone ossification and tumor growth. Several techniques have been proposed to surmise high resolution image from a low resolution image but either they lack accuracy or computational efficiency. Zigzag errors and the blurring effects are the most common effects observed in the super resolution image expansion. Sharpness and liberty from artifacts in edges are two crucial features in the perceived quality of images. Edge is the region in an image where discontinuities of luminance occur. Luminance varies sharply across the edge direction and gradually along the edge direction; hence pixel values have good correlation along edges and poor correlation across edges .
II. Related Work
Edge-directed interpolation (EDI) methods utilize the local statistical and geometrical properties to interpolate the unknown pixel values , , . In NEDI method  a hybrid approach is used to switch between bilinear interpolation and covariance-based interpolation. The Improved New Edge directed Interpolation (iNEDI) method  modifies the NEDI method by varying the dimension of the training window with respect to the edge size and uses a circular window instead of rectangular window to obtain better PSNR performance. The Iterative Curvature Based Interpolation (ICBI) method  considers the effects of the curvature continuity, curvature enhancement and isophote contour. In spite of the impressive performance, the augmented computational complexity of covariance-based adaptation is prohibitive. Conventional linear interpolation schemes (e.g., bilinear and bicubic) based on space-invariant models fail to capture the rapid evolving information around edges and therefore generate interpolated images with artifacts and blurred edges. Linear interpolation is generally preferred for computational simplicity while non linear interpolation is preferred for performance . Researchers have accomplished enhanced image quality by performing edge directed interpolation by modifying the interpolation scheme . In  we proposed a novel scheme which uses bicubic interpolation and two-dimensional (2D) filtering with a unique interpolation method to produce accurate and perceptually pleasant super resolution image. In this paper we evaluate the performance of the proposed algorithm by comparing PSNR and MSE with the conventional linear interpolation methods. The proposed scheme was applied to digital X-Ray images that were obtained from GE Healthcare. The results show improvement in PSNR and MSE performance of digital X-ray images based on our scheme.
The most vital detail in an image is edge, thus to maintain a sharp image, loss or smoothness of edges should be avoided. The linear interpolations techniques are well known for their efficiency over non linear interpolation techniques but lack the quality of performance produced by the nonlinear interpolation techniques. Thus to overcome the poor performance of linear interpolation technique we propose an interpolation technique that uses filter to preserve edges. Bilinear [1 1]/2 and the 6-tap filter [1 -5 20 20 -5 1] /32 are well known filters used in the H.264 coding standard. The 6-tap filter [1 -5 20 20 -5 1] /32 in equation (1) was used in our work due to better performance and high pass characteristics to obtain sharp digital X-ray images . In  characteristics of interpolation filter design have been discussed.
Our scheme works in the following three phases as shown in Fig. 1, Fig. 2 and Fig. 3. In the first stage bicubic interpolation is performed on a low resolution image to generate a high resolution image. Next this image is passed through a 6-tap filter with coefficients [1 -5 20 20 -5 1] to produce a filtered image. In the second stage column interpolation is performed by using bicubic interpolated image and the filtered image obtained from the first phase. Next this column interpolated image is passed through the 6-tap filter mentioned above to obtain the final filtered image. In the third stage row interpolation is performed to generate super resolution image by using column interpolated image and final filtered image obtained from the second phase. For an RGB image the entire process is applied to all the layers respectively to produce the final super resolution image. The choice of the 6-tap filter with coefficients [1 -5 20 20 -5 1] has been made due to the fact that it has more high pass and less low pass behavior which preserves edges in an image . The bicubic interpolation merged with 2D interpolation filter preserves and refines the edges of the image to produce high quality images. Bicubic interpolation combined with 2D filtering with a unique interpolation method yields impressive results. The filter2 command of MatLab is used for 2D filtering of image; it performs 2D correlation and yields the central component of the correlation as the outcome that is of equal dimension as the input image. The 2D correlation is performed by implementing 2D convolution with the filter coefficient rotated 180 degrees . Thus the filter2 rotates the 6-tap filter with coefficients [1 -5 20 20 -5 1] 180 degrees to create a convolution kernel, it then calls conv2, the 2D convolution function of MatLab, to implement the filtering operation. By default, filter2 then selects the central component of the convolution that is the same size as the input image, and returns this as the result . The improved PSNR performance and visual quality of digital X-Ray images shows the effectiveness and accomplishment of the proposed scheme.
IV. Experimental Results and Discussions
The set of seven digital X-ray RGB images shown in figure 4 taken from GE healthcare were used to compare the performance of our scheme with bilinear, bicubic, and nearest neighbor interpolation methods . The seven digital X-ray RGB images were enlarged with an enlargement factor of 4X by using bilinear, bicubic, and nearest neighbor by Trung Duong  and MatLab's built in command "imresize" and proposed interpolation scheme. The 4X enlarged digital X-ray RGB images of skull is shown in figure 5 for visual comparison. The Peak signal to Noise Ratio (PSNR) of all the seven digital X-ray RGB images is shown in figure 6. The Peak signal to Noise Ratio (PSNR) of all the seven digital X-ray RGB images was calculated by using equation (2) .
The results show sharpness in the perceived quality of images and the effectiveness of the proposed method. We can observe that annoying ringing artifacts are dramatically suppressed in the interpolated images by our scheme due to 2D interpolation filtering. It can be observed that our scheme generates the image with the highest visual quality. In Fig. 6 PSNR (dB) values of 4X enlarged digital X-ray RGB images have been plotted in MatLab to show the improved performance of our scheme. The curves demonstrate the marked increase in PSNR with the proposed scheme versus the conventional linear interpolation methods. The curve of proposed method is clearly higher than the bilinear, bicubic and nearest neighbor interpolation methods. Peak signal to noise ratios (dB) and Mean Square Error (MSE) obtained by comparing images up-scaled by approximately 4X factor with reference images is summarized in table I and table II respectively. The new proposed method provided the best results with an average PSNR of 44.32017 dB for 4X enlarged RGB images. The proposed interpolation scheme with 4X enlargement factor obtained an average MSE of 2.881244 dB for 4X enlarged RGB images. The results for bilinear, bicubic and nearest neighbor interpolation techniques have been obtained with a Matlab implementation of the proposed algorithms. Thus our interpolation scheme is clearly superior to linear interpolation techniques. Statistical analysis of PSNR and MSE of 4X enlarged medical images has been shown in figure 7 and figure 8 respectively. The minimum value, maximum value, average (mean), median, mode, standard deviation (std) and range of proposed interpolation scheme has been compared with bilinear, bicubic and nearest neighbor interpolation techniques. Standard deviation is a measure of how widely values are dispersed from the average value (the mean). The lowest standard deviation value of PSNR and MSE with the proposed scheme shows the consistency of our scheme as compare to bilinear, bicubic and nearest neighbor interpolation techniques.
In this paper we presented a novel interpolation method for accurate single image interpolation of digital X-rays images. The edge artifact and over smoothing problem is alleviated and blurring is eliminated. The proposed method conquers the existing problems of linear interpolation by implementing 2D interpolation 6-tap filter. The performance of the proposed method has been confirmed with extensive simulation and assessment with ICBI and iNEDI interpolation methods. The results showed that the presented method has achieved exceptional perceptual performance with consistent PSNR performance.
Thanks to Andrea Giachetti and Nicola Asuni for providing ICBI and iNEDI implementation. Thanks to Patrick Vandewalle and Athanasopoulos Dionysios for their support.
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