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In this paper image quality of two types of compression methods, wavelet based and seam carving based are investigated. A metric is introduced to compare the image quality under wavelet and seam carving schemes. Meyer, Coiflet 2 and Jpeg2000 wavelet based methods are used as the wavelet based methods. Hausdorf distance based metric (HDM) is proposed and used for the comparison of the two compression methods instead of model based matching techniques and correspondence-based matching techniques, because there is no pairing of points in the two sets being compared. In addition entropy based metric (EM) or peak signal to noise ration based metric (PSNRM) cannot be used to compare the two schemes as the seam carving tends to deform the objects. The wavelet compressed images with different compression percentages were analyzed with HDM and EM and it was observed that HDM follows the EM/PSNRM for wavelet based compression methods. Then HDM is used to compare the wavelet and seam carved images for different compression percentages. The initial results showed that HDM is better metric for comparing wavelet based and seam carved images.

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 [

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) [

There are prominent reviews of image quality metrics have been done during the last few decades. The research done by, Ahumada [

In this research the authors have introduced the Hausdorf distance metric [

Wavelet based methods and seam carving were used as compression schemes. Where Meyer, Coiflet2 [

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 [

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 [

Seam carving is a technique targeting image compression and resizing based on detection of seams from the energy function of the image. The method aims at finding seams of minimum energy and manipulating the image by carving out these seams [

Effective resizing of images not only use geometric constraints, but consider the image content as well. Conventional image resizing consists of cropping or evenly down sampling that lead to loss of important features or distortion. Seam carving method enables us to remove pixels from uninteresting parts of the image while preserving important content. The cumulative energy function is defined by Equation (3).

And the backtracing in x direction can be represented mathematically as shown in Equation (4).

PSNR is used as a general metric to measure the quality of restoration of lossy or lossless compression of images. The signal denotes the original data, and the noise represents the error introduced by compression. However, a higher PSNR generally indicates that the reconstruction is of higher quality, in some cases it may not be true. The PSNR is defined as,

where,

The,

The entropy can be used as a statistical measure of uncertainty to characterize the texture of an image [

and is defined by a probability distribution

Hausdorf distance is a metric between two point sets [

Let

where,

and

The function

The Hausdorf distance

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 MatLabâ„¢ built in functions.

The

At 35%, r value of 0.98 and p value of less than 5% are observed. At 70%, r value of 0.98 and p value of less than 5% is observed. At 90% r value of 0.7 and a p value less than 5% is observed. Between the EM and HDM values a linear relationship is observed at 35% to 90% percentage compressions. Also at higher compression percentages above 90% less r lower than 0.7 were observed.

The EM vs. HDM data of the seam carved images are shown in

It was observed that change of the HD values is significant after 70% of compression. For all 7 images increasing HD values are observed with the compression percentage.

The tabulated data are show in

Regression results of HD values of Meyer and Coiflet 2 based compressed images at different compression percentages.

Meyer | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

%/Image | I1 | I2 | I3 | I4 | Veg | ARC | Lena |

90 | 26.5100 | 48.0288 | 39.0115 | 36.8217 | 29.2913 | 24.4681 | 33.3597 |

70 | 20.5646 | 19.4164 | 35.7021 | 26.4261 | 24.6625 | 10.7999 | 19.5647 |

35 | 20.1920 | 18.4900 | 35.3676 | 25.6988 | 23.4181 | 10.4833 | 19.2474 |

Coiflet 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

%/Image | I1 | I2 | I3 | I4 | Veg | ARC | Lena |

90 | 26.6915 | 47.9993 | 39.0464 | 36.8609 | 33.2415 | 21.9770 | 35.1994 |

70 | 20.7846 | 18.9458 | 36.2383 | 24.7841 | 23.7192 | 10.6456 | 19.8867 |

35 | 20.0454 | 18.3209 | 35.6226 | 24.7692 | 23.3485 | 9.9282 | 19.4559 |

Compression | r | Slope |
---|---|---|

90% | 0.97 | 1.009 |

70% | 0.99 | 1.007 |

35% | 0.99 | 1.022 |

The HD data of the JPEG2000 and seam carving schemes are shown in the

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

JPEG2000 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

%/Image | I1 | I2 | I3 | I4 | Veg | ARC | Lena |

90 | 28.6612 | 27.5430 | 59.1172 | 37.2640 | 28.1909 | 7.8966 | 28.3545 |

70 | 22.6684 | 26.2677 | 53.0732 | 31.7846 | 28.0308 | 12.7279 | 25.2784 |

35 | 18.9420 | 19.6696 | 34.8550 | 24.5547 | 22.5037 | 9.3246 | 20.5279 |

Seam | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

%/Image | I1 | I2 | I3 | I4 | Veg | ARC | Lena |

90 | 42.4345 | 40.2480 | 59.9495 | 37.1812 | 30.3892 | 19.7472 | 27.4945 |

70 | 32.8792 | 34.8564 | 56.7495 | 33.1015 | 25.1887 | 16.4422 | 25.4391 |

35 | 27.4615 | 32.0450 | 50.9405 | 29.6577 | 18.4954 | 12.6534 | 22.4391 |

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 (

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 (

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.

However images with comparatively close energies of the seams, the comparison of seam carved and JPEG2000 is reversed. In

Compression | Seam Carving | JPEG2000 | ||
---|---|---|---|---|

HDM | PSNR | HDM | PSNR | |

90% | 37.1812 | 6.4422 | 37.2640 | 25.5595 |

70% | 37.1015 | 12.5210 | 31.7846 | 29.5958 |

Compression | veg | I_{4} | ||
---|---|---|---|---|

HDM | PSNR | HDM | PSNR | |

90% | 30.3892 | 9.9555 | 37.1812 | 6.4422 |

70% | 29.1887 | 10.3333 | 37.1015 | 12.521 |

Compression | Seam Carving | JPEG2000 | ||
---|---|---|---|---|

HDM | PSNR | HDM | PSNR | |

90% | 42.435 | 14.377 | 28.7 | 23.811 |

70% | 32.879 | 13.848 | 22.7 | 28.6135 |

PSNR shows a higher difference and can be seen from the

Also in

In _{1} and I_{2} 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.

Compression | Arc | Train | ||
---|---|---|---|---|

HDM | PSNR | HDM | PSNR | |

90% | 19.7472 | 6.2862 | 59.9495 | 10.2722 |

70% | 19.4422 | 8.6968 | 59.7495 | 9.4208 |

Compression | I_{1} | I_{2} | ||
---|---|---|---|---|

HDM | PSNR | HDM | PSNR | |

90% | 42.4345 | 14.3768 | 40.2480 | 9.6638 |

70% | 32.8792 | 13.8482 | 34.8564 | 9.7073 |

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