The rapid growth of wireless communication systems has increased the demand for robust multimedia transmission with better quality, coverage, and more power and bandwidth efficiency. The restriction of the wireless communication channels like limited bandwidth increases the demand for more reliable and better quality multimedia communication systems, specifically to develop transmission techniques that do not consume more bandwidth while achieving better received image quality. One way of sending high-quality images through band limited wire/wireless communication channels can be achieved by applying the proper compression technique depending on the transmission capacity, type of the image and the download time of the file as the independent variables [1]-[3]. The proper compression technique can be identified as the selected method of compression and the respective compression percentage according to a metric.

The evaluation of lossy techniques is extreme difficult when describing the type and amount of degradation in reconstructed images. Due to the problems related with the subjective measures of image quality, there are lots of research has been done in order to develop a reliable quantitative measure.

The most commonly used metric for measuring compression is based on image quality which can be defined as signal to noise ratio (PSNR) or mean squared error (MSE) [18]. However, they often fail when evaluating the image quality with different compression techniques. Even more importantly, the metrics do not measure object shape or boundary variations such as edges due to the compression techniques.

There are prominent reviews of image quality metrics have been done during the last few decades. The research done by, Ahumada [4] provides a concise summary of perceptual metrics applied to image quality research. Jayant et al. [5] describe how perceptual characteristics have been applied to signal compression. The research work by Daly [6] provides a number of visual factors which should be integrated in a perceptual metric in order to evaluate image quality. According to Eskicioglu [7] have proved a number of quality metrics. The research done by S. Fernando and R. Wijesiriwardana [8] has showed how entropy can be used as a metric [EM] to evaluate loss of information due to compression techniques such as wavelet based methods and seam carving. However due to the image geometric complexities EM methods found to be difficult to use in seam carved method [8].

In this research the authors have introduced the Hausdorf distance metric [9] to assess the change of images due to compression techniques such as wavelet based method and seam carving by computing the amount of resemblance of shape of the objects.

Wavelet based methods and seam carving were used as compression schemes. Where Meyer, Coiflet2 [10], [11], and JPEG2000 [12] wavelets based compression methods were experimented together with an energy based seam carving method [13].

In order to select a proper method out of the methods used a metric is required and EM based metrics have been researched for the wavelet transformation based methods [14]-[17]. However when comparing seam carving method and wavelet methods a new metric is required as EM based metrics is not ideal for measuring the quality of the seam carved image as pixel coherence is preserved and only the shapes are distorted in a seam carved image. Moreover model based or correspondence based matching techniques cannot be used as the number of points being different on compressed images. Therefore we used Hausdorf distance based metric (HDM) [9] to compare the compressed images.

First part of this research we compare the wavelet based compression methods with EM and HDM and It was found out that they are comparable. Hence HDM can be used as a valid metric to measure the image distortion in wavelet based compressed images.

The second part of the research we used HDM to compare energy based seam carved images with different compression percentages and it was found that HDM is a good metric to compare the image distortion in seam carved images.

The third part of the research we have compared the Meyer, Coiflet 2, JPEG2000 and seam carved images based on HDM. The theory, method and the results are discussed in the following chapters.

The rapid advancement in wavelet technology has led to advanced standards for image compression which is based on discrete wavelet transform (DWT). It has brought a new surge of interest in wavelets and also towards advancement and faster computational algorithms for storing and transmission of images

In this research two families of wavelets namely, Meyer and Coiflet 2 wavelets and JPEG2000 are used for the compression. The Equations (1) and (2) shows the Meyer scale and wavelet functions and JPEG2000 is based on defined two wavelet transformations namely CDF9/7 and CDF(5/3). Each layer of JPEG2000 adds coded information to improve the quality of the image [12].

Different types of images are selected for the testing. The images are selected so that they will cover the common types of photographic images. The compression percentages of 35%, 50%, 70% and 90% are used for each type of image respectively and the entropy and Hausdorf distance were calculated by using MatLab™ built in functions. Figure 1 shows the 7 images used.

The initial experimental data showed HDM can be used as a metric in different compression schemes specially to measure the quality of the seam carved images. However more testing is required with different image types to justify HDM as a Metric for comparing different compression schemes.

In addition seam carved images showed better image quality in identifying objects over 70% compression

percentages with respect to Meyer and Coiflet 2 wavelet based compression schemes. Moreover with images having textual data seam carved images preserved the information better than the Meyer or the Coiflet 2 schemes images at the same compression percentage (Figure 10). The images with large curved objects were severely distorted under the seam carved scheme (Figure 11) above 90% compression.

Comparing 90% compression of seam carving and JPEG2000, the JPEG2000 shows the entire image while seam carving has removed low energy plane areas while preserving high energy geometrical details (Figure 12).

The following table shows how the HDM varies based on two compression techniques.

In JPEG2000 at 90% the detail features which shows the geometry or shape of the buildings has considerably been removed while seam carving preserves the detail geometry and the hue of the high energy objects. Table 4 shows that there is not much difference (0.21%) in HDM for seam carving while JPEG2000 shows a considerable change (17.24%) of HDM from 70% to 90%. Table 5 also has similar results. Which is a good indication of HDM being a better metric than that of PSNRM that depend on the hue and the noise.

However images with comparatively close energies of the seams, the comparison of seam carved and JPEG2000 is reversed. In Figure 13, seam carving has removed seams from the objects thereby changing the geometry or shape of the object. However, the JPEG2000 removes detail geometry and hue contrast from the image while preserving overall image features.

Table 6 shows this shape or geometrical difference with HDM while the PSNRM is unable to measure this variation as PSNR is increased in seam carved image and decreased in JPEG2000 image without any coherence with the geometrical variation of the two images. In addition even though the HDM has increased in under the both schemes, the effect of lower HDM variation (25% in JPEG2000 compressed and 30% in seam carved) is an indication of better preservation of geometry in the JPEG2000 compressed images for images with lower seam energies.

Figure 14 shows the compression of images using seam carving at 70% and 90%. Here we can observe that when compression increases the seams from sky area has been removed dominantly. This affects the image geometry in a minimum level and thus the HDM values does not show considerable change. However, the

PSNR shows a higher difference and can be seen from the Table 4.

Also in Table 7 and Table 8 it can be clearly seen that the PSNRM is not a good metric with the percentage compression as the variation of the values are inconsistence from image to image. This is another indication that HDM is a better metric than the PSNRM at higher compression percentages.

In Figure 15, the images I₁ and I₂ has less variation in energy seams. Therefore when compressing at 70% and 90% seams containing geometrical features (mainly edges representing the object shape) has removed. Thus resulting a considerable change in shape. Both JPEG2000 and seam carving method can preserve the textual data.

Further we observed that the I2 PSNR and I1 PSNR are inconsistent and HDM maintained its consistency.

Based on these results we can conclude that the HDM is a better metric for representing geometrical or shape changes due to image compression techniques at compression percentages above 70%.

S. Fernando,R. Wijesiriwardana, (2016) Analysis of Wavelet Compression and Seam Carving Using the Hausdorf Distance. Journal of Computer and Communications,04,35-45. doi: 10.4236/jcc.2016.43006