**7.1 Fractal image compression with WPA**

The resolution presents an aspect that should not be ignored when trying to test the efficiency of an approach. For our circumstance, we will take into consideration the three test images (Lena, Barbara, and cameraman) with different resolutions (16 \* 16, 32 \* 32, 64 \* 64, 128 \* 128, 256 \* 256) so that we can see the impact of this factor on the quality quantities (compression ratio, compression time, EQM, PSNR) (**Figures 1** and **2**).

From the test images with a reconstructed resolution of 256 \* 256, it can be seen that the quality of the images is acceptable to a very good degree. And to be more exact, we must refer to calculable measures.

The table below presents the results obtained by applying our approach to the above images with different resolutions:

**Figure 1.** *Tested images (before compression). (a) Cameraman, (b) Lena, and (c) Barbara.*

**Figure 2.** *Decompressed tested images (after WPA compression). (a) Cameraman, (b) Lena, and (c) Barbara.*

The results obtained (detailed in **Table 1**) illustrate firstly the agreement between image resolution and encoding time, which demonstrates that our proposed method is significantly responsive to image resolution; it is also clear that the image quality is in contrast linked to it (image quality degrades quickly as resolution increases). This is clearly shown by the amplitudes of the PSNR and the MSE.

The compression ratio remains relative to the resolution where we indicate that our method interferes in this measurement. Wolves appear when the quantity of blocks is very huge (higher resolution) by contributing a higher compression rate than that existing in lesser resolutions.

Decompression time stays optimized and is similar for almost all methods. This is due to the decompression process which is not complex compared to the compression process.

**7.2 Using bat-inspired algorithm to enhance fractal image compression**

Lena in order to extract the adequate number of bats that will be used in our

**Compression time**

approach.

**11**

**Table 2.**

that will be used in our algorithm.

**bats**

**Images Number of**

*Comparison of the FIC-WPA with other techniques.*

*Optimization of Fractal Image Compression DOI: http://dx.doi.org/10.5772/intechopen.93051*

**Bat's number:** In **Table 3**, we will examine the images of the cameraman and

**Images de test Methods PSNR (dB) Time (s) Ratio (CR)** Lena 128\*128 FIC-WPA 32.641 34.257 1.480

Lena 256\*256 FIC-WPA 33.305 668.810 1.596

Cameraman 256\*256 FIC-WPA 31.605 774.438 1.741

Barbara 128\*128 FIC-WPA 32.348 22.713 1.310

Barbara 256\*256 FIC-WPA 33.288 509.406 1.447

Suman K. Mitra et al.'s works [7] 30.22 / 1.059 Vishvas V. Kalunge et al.'s works [42] / 67 /

Y. Chakrapani et al.'s works [37] 26.22 2370 1.3 Exhaustive search 32.69 8400 1.3 DWSR [31] 25.8212 56.4247 1.56355 PSO-RCQP [43] 27.089 6.453 1.6392

Vishvas V. Kalunge et al.'s works [42] / 66 /

Y. Chakrapani et al works [37] 28.34 2500 1.2 Exhaustive search 32.84 8400 1.2

PSO-RCQP [43] 26.686 268 1.8212

**Loudness: Table 4** presents some tests carried out on an additional stress which is loudness, with the objective of taking into consideration the good value for the test. **Frequency:** The last test table (**Table 5**) is made to pick up the best frequencies

> **Decompression time**

 0.459 0.707 1.366 30.934 8.563 0.452 0.729 1.372 31.216 9.417 0.451 0.749 1.349 30.934 8.879 0.509 0.843 1.355 29.827 10.045 0.472 0.919 1.365 30.412 10.405 0.478 0.749 1.348 31.895 9.663 0.475 0.883 1.335 30.989 8.899 0.457 0.750 1.392 29.997 9.870

4 0.548 0.727 1.315 30.083 15.612 8 0.505 0.716 1.311 30.071 14.929

Cameraman 2 0.488 0.705 1.385 31.608 10.088

Lena 2 0.518 0.739 1.303 30.629 14.440

**Compression ratio**

**PSNR MSE**

We will now focus on comparing our proposed method with some other techniques. The following table (**Table 2**) shows the notable alteration between our method and the others:


#### **Table 1.**

*Variation in image resolution.*


#### *Optimization of Fractal Image Compression DOI: http://dx.doi.org/10.5772/intechopen.93051*

**Table 2.**

The results obtained (detailed in **Table 1**) illustrate firstly the agreement between image resolution and encoding time, which demonstrates that our proposed method is significantly responsive to image resolution; it is also clear that the image quality is in contrast linked to it (image quality degrades quickly as resolution increases). This is clearly shown by the amplitudes of the PSNR and the MSE.

*Decompressed tested images (after WPA compression). (a) Cameraman, (b) Lena, and (c) Barbara.*

than that existing in lesser resolutions.

*Fractal Analysis - Selected Examples*

**Resolution Compression**

**time (s)**

compression process.

method and the others:

**Tested image**

**Figure 2.**

**Table 1.**

**10**

*Variation in image resolution.*

The compression ratio remains relative to the resolution where we indicate that our method interferes in this measurement. Wolves appear when the quantity of blocks is very huge (higher resolution) by contributing a higher compression rate

Decompression time stays optimized and is similar for almost all methods. This

We will now focus on comparing our proposed method with some other techniques. The following table (**Table 2**) shows the notable alteration between our

Cameraman 16\*16 0.184 0.818 1.098 2.617 37.999

Lena 16\*16 0.185 0.832 1.095 7.730 33.616

Barbara 16\*16 0.225 0.812 1.019 1.352 38.070

**Decompression time (s)**

32\*32 0.446 0.802 1.174 4.079 36.173 64\*64 2.451 0.816 1.420 6.853 31.509 128\*128 41.284 0.810 1.653 8.931 30.096 256\*256 774.438 0.897 1.741 9.152 31.605

32\*32 0.507 0.801 1.125 5.861 34.451 64\*64 2.290 0.791 1.287 8.401 33.550 128\*128 34.257 0.821 1.480 9.547 32.641 256\*256 668.810 0.850 1.596 9.282 33.305

32\*32 0.607 0.763 1.055 4.064 36.067 64\*64 1.868 0.781 1.152 6.259 35.060 128\*128 22.713 0.793 1.310 11.093 32.348 256\*256 509.406 0.861 1.447 11.115 33.288

**Compression ratio**

**MSE PSNR (dB)**

is due to the decompression process which is not complex compared to the

*Comparison of the FIC-WPA with other techniques.*
