Hidden Influences on Image Quality when Comparing Interpolation Methods

Emil Dumic, Sonja Grgic and Mislav Grgic University of Zagreb, Faculty of Electrical Engineering and Computing,

Department of Wireless Communications Unska 3/XII, HR-10000 Zagreb, Croatia

E-mail: emil.dumic@fer.hr

Keywords: Image Interpolation, Image Quality, Wavelets, B-spline Abstract - When comparing different interpolation methods, common approach is to use an objective image quality measure that evaluates the numerical errors between the original image and interpolated image. The problem with this approach is impossibility to have original image in two or more different resolutions. Common method is to start with an original image, calculate a lower resolution version of original image (downscaling), and then use different interpolation methods to magnify low resolution image (upscaling). After that original and magnified interpolated images are compared to evaluate difference between them. In our research we found that downscaling process has great influence on results of upscaling. This influence is not properly addressed in references that deal with image interpolation methods. Therefore in this paper we will try to examine how the process of achieving lower resolution image affects picture quality of interpolated images. Our results show that comparison of image interpolation methods depends on downscaling technique, image contents and quality metric.

1. INTRODUCTION

Image interpolation is a method of constructing new data points within the range of a discrete set of known data points. It is a key aspect of digital image processing and it is used in other, more complex image processing techniques such as translation, scaling, rotation etc., in which we need to determine new, interpolated pixels (picture elements) which do not exist in the original, reference image [1]. Interpolated pixels can be computed as a linear combination of weighted functions (interpolation kernel) and known pixels.

Quality of image interpolation methods can be evaluated using different measures. The best way to do this is by making visual experiment, under controlled conditions, in which human observers grade which image provides better quality. Such experiments are time consuming and costly. Much easier approach is to use some objective measure that evaluates the numerical errors between the original image and interpolated image [2]. In real world, there is no perfect way for objective assessment of magnification quality [3]. The image that should be magnified using some interpolation method is of fixed resolution. Interpolated image that is result of magnification has different (larger) resolution. The objective picture quality measures are computed on the basis of known original image under condition that original and interpolated images are of the same size. When interpolation method is used to produce magnified image, interpolated image (magnified original image) will not be of the same size as original. In this case interpolated (large) image can not be compared with original (small) image. To compute objective image quality

measure, original image of interpolated (large) image need to be known or simulated. Usually we start with an original image, generate a lower resolution version of original image (downscaling) and then use different interpolation methods to magnify it (upscaling). Then we compare the magnified, interpolated image with the original image [3-7] to prove that some new interpolation method works better than other methods. The process of downscaling also affects image quality. This hidden influence on image quality should be taken into account when comparing interpolation methods.

In this paper error between original and interpolated image is analyzed using various picture quality measures. Our results show that quality measures depend mostly on downscaling method. Most often, authors do not pay attention to this very important factor or even do not mention it. Of course upscaling can also improve or degrade results, but not as much as downscaling.

There are several ways how to downscale original image to generate its lower resolution version. For example, A. Munoz et al. [4] use the same interpolation method for downscaling and upscaling and compare original and interpolated image. Similar method is used in [5]. A little different approach is proposed by D.D. Muresan et al. in [6] where one specific interpolation method (Daubechies 1, which is in fact the same as bilinear) is used for downscaling and then different methods for upscaling. Some authors propose image rotation instead of scaling [1].

In this paper we examine how the process of achieving lower resolution image over three different resolutions using different interpolation methods affects picture quality of interpolated images. The paper is organized as follows. In section 2 different methods for image interpolation and picture quality measures are presented. Section 3 compares picture quality results for different downscaling and upscaling techniques in three different resolutions. Section 4 draws the conclusion.

2. INTERPOLATION METHODS AND IMAGE QUALITY MEASURES In our research we used three different interpolation

methods for image resampling:

• bilinear [1] • B-spline [1] • TVC10_18 wavelet filter [7].

Bilinear and B-spline are two common interpolation methods used in image resampling. With bilinear interpolation interpolated pixels (picture elements) are computed using four nearest known samples (two in horizontal by two in vertical direction). B-spline interpolation uses sixteen nearest samples (four by four in each direction). Because B-spline synthesis function isn't interpolant, it is needed to transform the input pixels into other coefficients, so that final interpolation gives good results. The drawback is the need for an additional step, usually recursive digital filter, thus resulting in longer computational time. This is however compensated by the gain in final results which are generally better in comparison with interpolating synthesis functions [1].

Our previous research has shown that wavelet filters can be also used for image resampling [7]. Reconstruction filter (mirror lowpass filter) can be used for image magnification and analysis filter (lowpass filter) for image minification. Wavelet filters have good interpolation properties, because of their design and fractal nature. Generally discrete wavelet decomposition and reconstruction in two dimensions (because in image transform we have two dimensions, width and height) can be described in Fig. 1 [8]. Decomposition is done with separable wavelet transform, which is in fact one dimensional convolution with subsampling by factor 2 along the rows and columns of image. Reconstruction is done reversely. This means upscaling by 2 and then convolution along the rows and columns.

L

H

↓2

↓2

L

↓2

↓2

H

L

↓2 H

↓2 ↑2

H'

L'

↑2

↑2

H' ↑2

L' ↑2

↑2

L'

H'

aj aj aj+1

dLH,j+1

dHL,j+1

dHH,j+1

Analysis Synthesis

Rows Columns Rows Columns

Fig. 1. Wavelet decomposition and reconstruction In Fig. 1 L is lowpass analysis filter (from scaling

function), H highpass analysis filter (from wavelet function), L' and H' lowpass and highpass reconstruction filters, a approximation coefficients, d detail coefficients and ↓2 and ↑2 downscaling and upscaling by factor 2.

Firstly we presume that original image represent approximation coefficients aj at scale j. We downscale it using lowpass analysis filter, Fig. 2(a). Then we take lowpass coefficients which represent approximation of an original image, but with two times smaller width and height. If analysis filter is normalized by factor √2, then final picture will be about two times brighter in comparison with original picture. Thus it has to be multiplied by factor 0.5. The second possible approach is to calculate mean of all pixels of the original and final picture, find their ratio and multiply final picture by this ratio. Afterwards lowpass

coefficients, which represent interpolated picture with two times smaller width and height, should be upscaled, presuming that all detail coefficients are the same sizes as approximation, but are equal to 0, Fig. 2(b). If all these coefficients are reconstructed into one higher level, we get again the same image, with the same width and height as the original image. Again, if reconstruction filter is normalized by factor √2, we need to multiply it by factor 2.

In Fig. 2 ↓2 is downscaling, ↑2 is upscaling, "X" is multiplication by corresponding factor, L is analysis lowpass filter and L' is synthesis lowpass filter. If it is needed, algorithm for downscaling, Fig. 2(a) or algorithm for upscaling, Fig. 2(b) can be used again, where new original image is old interpolated image. This way we can compute images of different resolutions: two, four or eight times smaller than the original image (using Fig. 2(a)) and afterwards two, four or eight times larger (using Fig. 2(b)) so that final interpolated image is of the same size as original image.

L ↓2 ↓2 L X0.5

Rows Columns

Original image

Interpolated image

2x smaller (a)

L' ↑2 ↑2 L' X2

Rows Columns Interpolated

image 2x smaller

Interpolated image

(b)

Fig. 2. Wavelet based image interpolation: (a) downscaling,

(b) upscaling When using three above mentioned image interpolation

methods for image resampling, original image is downscaled by a factor 2, 4 or 8 to generate low resolution version of original image, Fig. 3. Low resolution image is magnified using different methods by the same factor used for downscaling (X is equal to two, four or eight). To be able to compare them with standard interpolations, we used bilinear [1] and B-spline [1] interpolation described above. All test images have original resolution 2048x2048 pixels. Mentioned interpolation methods are used first for downscaling in three resolutions: 1024x1024, 512x512 and 256x256 pixels. Afterwards each of the computed low resolution images is upsampled to its original size, 2048x2048 with all interpolation methods.

↓x ↑x

SNR, PSNR, PQS, SSIM

Original image

Interpolated image

Fig. 3. Image interpolation test setup

To be able to compare original and interpolated image, we used 4 image quality measures:

• SNR (Signal to Noise Ratio) [1] • PSNR (Peak Signal to Noise Ratio) [2] • PQS (Picture Quality Scale) [9] • SSIM (Structural Similarity Index) [10].

SNR is the ratio between the average power of a signal and the power of corrupting noise while PSNR is the ratio between the maximum possible power of a signal and the power of noise. SNR and PSNR are usually expressed in terms of the logarithmic decibel scale and they can be expressed as:

yx

baMSE

MSEPSNR

ba

aSNR

i jjiji

i jjiji

i jji

⋅

−=

=

−=

∑∑

∑∑∑∑

)(

255log10

)(log10

2,,

2

10

2,,

2,

10

(3)

In expressions ai,j and bi,j are pixels from original and interpolated image. x and y describe height and width of an image. MSE stands for Mean Square Error.

PQS is based on image features that affect image perception by the human eye [9]. PQS is constructed by regressions with Mean Opinion Score (MOS) that is measure of subjective picture quality with 5-level grading scale. PQS can take any value between 0 and 5 (grade 5 means excellent quality and grade 0 means unacceptable quality).

The Structural Similarity (SSIM) is a novel method for measuring the similarity between two images [10]. The SSIM can be viewed as a quality measure of one of the images being compared, while the other image is regarded as of perfect quality. It can give results between 0 and 1, where 1 means excellent quality and 0 means poor quality.

3. RESULTS

We compared interpolation methods using 4 test images: Andromeda [11], Tree, Train and Roof image with original resolution 2048x2048 pixels, Fig. 4. Results are shown in Tables I-IV. Results show that there are many different factors that can improve or degrade final results. Exclamation mark (!) after some PQS measures means that some of the weighting factors are out of their designed range, so PQS could give inaccurate values. Sometimes these inaccurate results are generally bad (usually below 1) and sometimes excellent (above 5).

All results depend on downscaled resolution, as well as type of an image, Tables I-IV. The comparison of images on some fixed downscaling resolution can't be made using all objective measures. For downscaling resolution 1024x1024 PQS usually gives results above 5 and for 256x256 results are under 0. These results are not valid. If we look SSIM measure on one fixed upscaling method, differences are generally too small (sometimes they can be noticed just on third decimal). SSIM is not enough sensitive measure and can't give precise results if differences

between interpolated images are small. If we look different image quality measures for the same image, some important results can be stressed. For all downscaling resolutions, we get almost always the best results by using TVC10_18 wavelet filter for downscaling. It can be also seen that different downscaling methods for fixed upscaling method make bigger differences among measures than different upscaling methods for fixed downscaling methods. This can be observed in Figs. 5-7 for Andromeda image and Figs. 8-10 for Roof image. All this images represent absolute difference between original and interpolated picture, where white areas represent small or no difference and darker areas represent bigger difference. The parameters used in parts (a) and (b) of Figs. 5-10 (images that use B-spline for downscaling) always give worse results than parameters used in parts (c) and (d) of Figs. 5-10 (images that use wavelet interpolation for downscaling). But, if we analyze only upscaling method, with the same downscaling (this means comparing (a) with (b) and (c) with (d)) it can be seen that results are similar. It proves that downscaling method determines image quality more than upscaling method.

(a) (b)

(c) (d) Fig. 4. Test images: (a) Andromeda, (b) Tree, (c) Train, (d) Roof image

The best PSNR and SNR results are obtained for images which don't have many details and for images that are downscaled to only half of its original size. Andromeda and Tree images give worse PSNR, SNR and PQS results in comparison with Train and Roof images. Train and Roof images have more uniform surfaces, unlike Andromeda and Tree images that have more edges and details. But if we consider SSIM measure results are not the same. Now, Andromeda image gives better results than other images and Tree image gives poorer results that other images. For example, if we compare differences between Andromeda and Train image, we can see that Andromeda has approximately 10 dB lower SNR and PSNR, and 0.03 higher SSIM than Train image. SNR and PSNR depend on pixel value distribution and can not be used for comparison of images with different contents. SSIM takes into account properties of human visual system (HVS) and does not depend on pixel value distribution. SSIM can be used for comparison of images with different contents. Picture of differences is shown in Fig. 11. Andromeda image has bigger difference (smaller PSNR and SNR) than Train image but SSIM for Andromeda image is higher than SSIM for Train image. Structural errors in Andromeda image are not so significant for HVS as errors in Train image. Usage of only PSNR or SNR as image quality measures can lead to wrong conclusions when comparing interpolation methods for different test images.

Andromeda image, resolution

2048 → 1024 → 2048 Andromeda image, resolution

2048 → 512 → 2048 Andromeda image, resolution

2048 → 256 → 2048 Upscaling

method Quality measure

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

SNR 17.13 17.25 17.43 12.53 12.38 12.85 7.87 7.80 8.61 PSNR 27.32 27.45 27.63 22.73 22.58 23.05 18.07 18.00 18.81 PQS 2.88 2.95 2.32 1.05 ! 0.36 ! 0.50 ! -6.58 ! -6.62 ! -7.70 !

Bilinear

SSIM 0.966 0.967 0.967 0.913 0.911 0.902 0.821 0.821 0.797 SNR 18.29 18.05 18.48 12.80 12.54 13.52 7.72 7.62 9.05

PSNR 28.48 28.25 28.68 23.00 22.74 23.72 17.92 17.82 19.25 PQS 2.99 2.60 2.66 1.37 ! 1.01 ! 1.74 -6.56 ! -6.74 ! -4.66 !

B-spline

SSIM 0.971 0.968 0.968 0.895 0.891 0.895 0.781 0.779 0.774 SNR 18.27 18.11 18.50 12.87 12.63 13.49 7.82 7.73 8.99

PSNR 28.46 28.31 28.70 23.07 22.83 23.68 18.02 17.93 19.19 PQS 3.19 2.91 2.96 1.32 ! 1.01 ! 1.70 -6.48 ! -6.58 ! -5.06 !

TVC10_18

SSIM 0.972 0.970 0.969 0.900 0.898 0.900 0.789 0.788 0.781

Table 1. Andromeda image

Train image, resolution 2048 → 1024 → 2048

Train image, resolution 2048 → 512 → 2048

Train image, resolution 2048 → 256 → 2048

Upscaling method

Quality measure

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

SNR 28.16 28.94 29.84 22.61 22.54 23.57 17.14 17.00 18.21 PSNR 36.45 37.23 38.13 30.90 30.83 31.86 25.43 25.29 26.50 PQS 4.67 4.91 5.06 ! 2.87 2.89 4.10 -2.25 ! -2.47 ! 1.20 !

Bilinear

SSIM 0.930 0.936 0.942 0.858 0.856 0.866 0.755 0.753 0.753 SNR 30.66 30.72 31.46 23.52 23.02 24.47 17.00 16.74 18.61

PSNR 38.95 39.01 39.75 31.81 31.31 32.75 25.29 25.02 26.90 PQS 5.31 ! 5.50 ! 5.51 ! 4.25 3.90 4.76 -2.29 ! -2.72 ! 1.39

B-spline

SSIM 0.946 0.943 0.952 0.863 0.853 0.872 0.744 0.738 0.751 SNR 30.25 30.56 31.52 23.45 23.08 24.57 17.14 16.91 18.67

PSNR 38.53 38.85 39.81 31.74 31.37 32.86 25.43 25.20 26.96 PQS 5.21 ! 5.43 ! 5.58 ! 4.02 3.80 5.19 ! -2.43 ! -2.78 ! 2.18

TVC10_18

SSIM 0.944 0.944 0.952 0.864 0.856 0.873 0.748 0.743 0.755

Table 2. Train image

(a) (b) (c) (d)

Fig. 5. Part of Andromeda image, downscaling 1024x1024: (a) B-spline downscaling and B-spline upscaling, (b) B-spline downscaling and TVC10_18 upscaling, (c) TVC10_18 downscaling and B-spline upscaling, (d) TVC10_18 downscaling and TVC10_18 upscaling

(a) (b) (c) (d)

Fig. 6. Part of Andromeda image, downscaling 512x512: (a) B-spline downscaling and B-spline upscaling, (b) B-spline downscaling and TVC10_18 upscaling, (c) TVC10_18 downscaling and B-spline upscaling, (d) TVC10_18 downscaling and TVC10_18 upscaling

(a) (b) (c) (d)

Fig. 7. Part of Andromeda image, downscaling 256x256: (a) B-spline downscaling and B-spline upscaling, (b) B-spline downscaling and TVC10_18 upscaling, (c) TVC10_18 downscaling and B-spline upscaling, (d) TVC10_18 downscaling and TVC10_18 upscaling

Tree image, resolution

2048 → 1024 → 2048 Tree image, resolution 2048 → 512 → 2048

Tree image, resolution 2048 → 256 → 2048

Upscaling method

Quality measure

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

SNR 19.80 20.20 20.42 15.77 15.56 16.24 13.19 13.02 13.96 PSNR 22.69 23.09 23.31 18.66 18.45 19.13 16.08 15.91 16.85 PQS 4.45 4.89 4.94 2.53 2.15 3.90 -4.68 ! -4.87 ! -0.54 !

Bilinear

SSIM 0.886 0.904 0.911 0.697 0.695 0.710 0.545 0.543 0.546 SNR 21.09 20.81 21.44 15.91 15.48 16.64 12.71 12.45 14.08

PSNR 23.98 23.70 24.33 18.80 18.37 19.53 15.60 15.34 16.97 PQS 5.15 ! 4.93 5.22 ! 3.26 2.76 4.59 -3.53 ! -4.05 ! 0.85 !

B-spline

SSIM 0.925 0.925 0.932 0.708 0.698 0.728 0.530 0.525 0.549 SNR 21.07 20.94 21.52 15.95 15.58 16.64 12.89 12.65 14.11

PSNR 23.96 23.83 24.41 18.84 18.47 19.53 15.78 15.54 17.00 PQS 5.02 ! 5.00 ! 5.34 ! 3.14 2.67 4.61 -3.64 ! -4.08 ! 0.98 !

TVC10_18

SSIM 0.922 0.926 0.933 0.709 0.701 0.728 0.534 0.530 0.551

Table 3. Tree image

Roof image, resolution 2048 → 1024 → 2048

Roof image, resolution 2048 → 512 → 2048

Roof image, resolution 2048 → 256 → 2048

Upscaling method

Quality measure

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

Bilinear downscale

B-spline downscale

TVC10_18 downscale

SNR 28.95 29.65 30.52 23.55 23.50 24.54 17.65 17.51 18.73 PSNR 37.25 37.95 38.82 31.85 31.80 32.84 25.95 25.81 27.03 PQS 4.81 4.99 5.12 ! 3.25 3.30 4.30 -2.36 ! -2.52 ! 1.37

Bilinear

SSIM 0.936 0.942 0.948 0.859 0.858 0.870 0.736 0.734 0.736 SNR 31.23 31.19 31.96 24.73 24.21 25.64 17.48 17.23 19.09

PSNR 39.53 39.49 40.26 33.03 32.51 33.94 25.78 25.53 27.39 PQS 5.36 ! 5.52 ! 5.53 ! 4.53 4.24 4.93 -2.21 ! -2.60 ! 2.08

B-spline

SSIM 0.952 0.951 0.958 0.873 0.864 0.884 0.730 0.725 0.743 SNR 30.87 31.07 32.02 24.59 24.22 25.71 17.63 17.41 19.17

PSNR 39.17 39.37 40.32 32.89 32.52 34.01 25.93 25.71 27.47 PQS 5.27 ! 5.46 ! 5.59 ! 4.30 4.14 5.33 ! -2.58 ! -2.91 ! 2.63

TVC10_18

SSIM 0.950 0.950 0.958 0.872 0.865 0.884 0.734 0.729 0.745

Table 4. Roof image

(a) (b) (c) (d)

Fig. 8. Part of Roof image, downscaling 1024x1024: (a) B-spline downscaling and B-spline upscaling, (b) B-spline downscaling and TVC10_18 upscaling, (c) TVC10_18 downscaling and B-spline upscaling, (d) TVC10_18 downscaling and TVC10_18 upscaling

(a) (b) (c) (d)

Fig. 9. Part of Roof image, downscaling 512x512: (a) B-spline downscaling and B-spline upscaling, (b) B-spline downscaling and TVC10_18 upscaling, (c) TVC10_18 downscaling and B-spline upscaling, (d) TVC10_18 downscaling and TVC10_18 upscaling

(a) (b) (c) (d)

Fig. 10. Part of Roof image, downscaling 256x256: (a) B-spline downscaling and B-spline upscaling, (b) B-spline downscaling and TVC10_18 upscaling, (c) TVC10_18 downscaling and B-spline upscaling, (d) TVC10_18 downscaling and TVC10_18 upscaling

(a) (b)

Fig. 11. Differences between original and interpolated picture, TVC10_18 downscaling interpolation to 256x256 pixels and same upscaling interpolation to 2048x2048 pixels for: (a) Train image (PSNR = 26.96 dB, SSIM = 0.755), (b) Andromeda image (PSNR = 19.19 dB, SSIM = 0.781)

From the corresponding tables, it can be also noticed that

for the same downscaling method, TVC10_18 and B-spline give similar results and only bilinear always give significantly worse results. The conclusion is that bilinear method isn't generally good for upscaling. Also, when B-spline is used for upscaling interpolation, bilinear interpolation seems to be somewhat better for downscaling, than B-spline. This is probably because bilinear interpolation computes interpolated pixel from only four nearest known pixels, unlike B-spline that uses sixteen.

From the above mentioned results it can be concluded that it is very important to exactly define downscaling interpolation. It can also be concluded that wavelet filters like TVC10_18 can be proposed for downscaling or upscaling interpolations, because they show good interpolation properties for simple and complex image contents. But, if we want only to magnify some image, B-spline also gives satisfactorily good results. Bilinear interpolation should generally be avoided for upscaling interpolation, except if computational time is very important. 4. CONCLUSION

In this paper we examined how different downscaling interpolation methods, quality measures and image contents influence on picture quality after upscaling interpolation. Our results show that for fair comparison of image interpolation methods, picture quality assessment should be properly defined, performed and analyzed. Otherwise, results of comparison can be incorrect. Our results show that downscaling method has great influence on results of upscaling. Therefore downscaling method should be precisely defined and performed. For overall evaluation of interpolation methods different quality measures and test images with different contents should be used to prove that some interpolation works well for different image types and quality metrics. Wavelet downscaling methods give good results for all measures and all images. It means that wavelet based downscaling techniques can be considered as

a good starting point for evaluation and fair comparison of interpolation methods. ACKNOWLEDGMENT

The work described in this paper was conducted under the research projects: "Picture Quality Management in Digital Video Broadcasting" (036-0361630-1635), and "Intelligent Image Features Extraction in Knowledge Discovery Systems" (036-0982560-1643), supported by the Ministry of Science, Education and Sports of the Republic of Croatia.

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[11] Test Image Andromeda, Available: http://www.spitzer.caltech.edu/ Media/releases/ssc2006-0/ssc2006-10b.shtml