Experimental Results

In this section, the proposed resizing technique will be compared with the method proposed by Y.S.

Park and H.W. Park [3] in two main aspects which are computational costs and visual quality of the resized images. The overall operations of the experiment are shown in Figure 5. The original image is in DCT domain and after process finished, the resized image in spatial domain is obtained and displayed.

The method [3] presented the algorithm in two cases called case I and case II which are only different in parameters selection. To resize images by a factor of ^{P Q}, it needs to upsize and downsize data by factors of ^P and ^Q, respectively. After that, IDCT is employed to retrieve the images in the spatial domain. It is seen that many procedures are required in [3] to achieve the displayed image In addition, this approach employs the fast forward and inverse DCT of composite length as given in [7-9].

Figure 5: Overall operations in the experimental implementation

In the experiment, a block size N =8 which is commonly used in images processing is selected.

Each tested image will be first downsized by a factor of P Q and subsequently upsized by a factor of Q P to evaluate the performance in term of PSNR. The overall operations are shown in Figure 5 using the naive DCT algorithms for impartiality. To avoid intervening influences from zero padding and truncation, a scaling factor (P Q) of [3] is selected.

Tables 1 and 2 show PSNR values and computational costs for downsizing by factors of 1 2 and 3 4, respectively. c_m and c_a stand for amounts of multiplier and adder used per pixel of the original images.

Table 1: Downsizing images by a factor of 1 2

Method Cost

((((

))))

Lena Peppers F-16

The proposed technique (6,5.25) 33.28 30.86 30.95

Bilinear (19.44,23.81) 31.40 30.20 29.01

Y.S. Park and H.W. Park [3] (case I) (8.97,16.53) 35.38 33.07 33.04

Y.S. Park and H.W. Park [3] (case II) (8.03,8.47) 34.72 32.58 32.28

Table 2: Downsizing images by a factor of 3 4

Method Cost

((((

))))

Lena Peppers F-16

The proposed technique (10.5,9.19) 39.14 36.00 38.48

Bilinear (22.05,27.52) 35.11 33.54 33.32

The method [3] (case I) (13.05,23.36) 40.76 37.43 40.15

The method [3] (case II) (11.68,16.14) 40.54 37.28 39.72

From Table 1 and 2, the proposed method requires the lowest computational costs for any resizing factors. The quality of images resized by the presented technique is lower than the method [3]

in term of PSNR valued, but higher than the spatially method. Although the proposed algorithm provides lower PSNR values compared to the DCT domain approach, the visual quality of images is acceptable over method in the spatial domain. It should be noted that, the method [3] use the fast DCT and IDCT for composite length in the resizing operation while others calculate in the naive way.

For another experiment, resizing images by arbitrary factors of P Q×R S is tested. P Q and R S are row and column resizing factors, respectively where P Q R, , and S are any integers. As given in [2-6], these algorithms in DCT domain need to resize images twice for arbitrary resizing. These methods consecutively upsizing images by P R× factors and downsizing images by Q S× factors or vice versa. In this experiment, the images are resolution of 1920x1080 [13]. The three tested images (Eye, Outdoor, Sunlight) are downsized to resolution of 720x480, 640x480 and 320x240 which are commonly used in many devices. Hence, the resizing factors are ^{4 9 3 8×} , ^{4 9 1 3×} and ^{2 9 1 6×} , respectively.

Table 3 and Table 4 show comparison of computational costs and PSNR values between the proposed method and the method [3]. The various factors (^{P Q×R S}) are indicated in the table. It is seen that the proposed method requires significantly lower computational costs in most cases compared to the method [3], except at factors of ^{2 9 1 6×} , the method [3] needs slightly lower number of multiplier because IDCT computation is very low for very small resizing factors. Although in term of PSNR, the method [3] is superior to the proposed technique in over all but the recovered version of the resized image obtained by the proposed technique is still perceptual acceptable. For example, the retrieved image after resizing at factor of ^{4 9 3 8×} obtained from the proposed method is illustrated in Figure 6.

Table 3: Computational costs

((((

))))

P Q R S×××× The proposed method method [3] (case I) method [3] (case II)

4/9x3/8 (4.33,3.79) (6.71,15.84) (5.84,6.66)

4/9x1/3 (3.85,3.37) (6.49,15.00) (5.46,6.43)

2/9x1/6 (1.63,1.43) (4.64,13.20) (1.49,2.00)

Table 4: PSNR values (dB) for downsizing by factors of P Q×R S

Figure 6: Retrieved image after resizing at factor of 4 9 3 8× obtained from the proposed method

7. Conclusions

This article presents an algorithm to resize images based on frequency scaling in the DCT domain.

Exploiting frequency scaling property makes periodicity and symmetric points occur which is analyzed by using the discrete Fourier transform. Hence, frequency scaling of the basis functions can be used to resize images. The experimental results show that the proposed method requires significantly lower computational costs as compared to other techniques. The proposed technique provides visual quality images better than the spatial domain method but the quality of resized images is lower than the method [3]. However, in practical, the proposed method is easily implemented because its complexity is extremely low. No additional hardware as well as additional computation is required. Therefore, it can be applied in real-time image processing or in high speed such as video streaming.

References

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ISSN 1450-216X / 1450-202X Vol. 101 No 3 May, 2013, pp.436-440 http://www.europeanjournalofscientificresearch.com