Abstract
In the field of image processing, there is an urgent need to adopt image transformations. In this paper, work is done on image coefficients after decomposing them through Curvelet transformations obtained through the fan filter. The research deals with two stages: the first is to study the effect of the Fan filter by adopting angles (8, 16, 32) on the image (Lina.jpg) of size (256*256) after being analyzed using Curvelet transformations at scales (2,3,4) through comparing a set of measurements (Contrast, Energy, Correlation, MSE, and PSNR) for both the original and reconstructed images. It can be found that Contrast and Energy criteria remain the same for the original and reconstructed images according to different levels of analysis or directions, so the value of the Correlation measure is 1. The value of the MSE criterion is very small and is almost not affected by the change of the number of angles in one scale, but it is slightly affected by increasing the scale analysis. What was mentioned above applies to the PSNR criterion as well. As for the second stage of the research, which included decomposing the image to its coefficients, canceling the effect of one of these coefficients, and then reconstructing it. The results proved that the two criteria (Contrast and Energy) were not affected with falling Correlation criteria from 1 to values ranging from (0.9987_0.9997) depending on the number of scales used in the Curvelet analysis and the number of angles used in Fan filter (8,16,32). The results also showed an increase in the MSE value when dropping some frequencies, and a corresponding decrease in the PSNR value. Whereas, the decrease in the MSE scale was demonstrated at a specific scale with the increase in the number of angles in the Fan filter, in contrast to the PSNR scale.
Highlights
As rapid developments in the last decades in information techniques that lead to the creation of enormous amounts of data images in various domains such as Exhibitions of fine arts, fashion design, medicine, and more
In the field of image processing, a minimum number of non-zero coefficients can accurately represent the unique properties of the image curve
The total number of coefficients will be 9 (as shown in Figure (5): one of the coefficients is in the first scale, and 8 in the second. It can be observed from these results that Contrast and Energy for both original and recovered images retain their values, and they are insusceptible at different scales: 2, 3, 4; and different angles: 8, 16, 32
Summary
As rapid developments in the last decades in information techniques that lead to the creation of enormous amounts of data images in various domains such as Exhibitions of fine arts, fashion design, medicine, and more. There was a need to innovate an effective method to retrieve image information to perform a special task and make an appropriate decision. The Curvelet Transform is one of the latest technologies that deal with the above [16]. In the field of image processing, a minimum number of non-zero coefficients can accurately represent the unique properties of the image curve. After analyzing the image using the Curvelet transform, most of the image information is concentrated in the coefficients. The energy is more concentrated, which results from analyzing the important characteristics of the image such as edge and composition.[3]
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