*4.3. Ranking of Aerial Image Lossy Compression*

After the alternatives were defined and qualitative criteria were calculated, the initial decision matrix for qualitative evaluation of the lossy compression of aerial images was formed. The example of the initial decision matrix for "img1" is presented in Table 2. As the matrix has negative values for the change of correlation, homogeneity, and energy, to make calculations consistent with WASPAS-SVNS, the rows with negative values were upshifted before the vector normalization. The obtained results by WASPAS-SVNS methodology described in Section 3.5 (steps 2–6) are presented in Table 3. The qualitative ranking of images' lossy compression was calculated using the utility function *S Q*e *i* (Equation (27)). Figure 7 presents the ranking of lossy compression for high and lowresolution images. Ranking of compression algorithms based on their qualitative suitability for the images makes it difficult to decide which compression ratios of lossy compression are unacceptable for visual inspection. Qualitative ranking by estimating the threshold of acceptable visual distortions places the algorithms with their compression ratios in order of priority, excluding those whose distortions are greater than the subjectively determined quality threshold (Table 3, Figure 8).


**Table 3.** Qualitative ranking of aerial images' lossy compression.

**Figure 7.** Qualitative ranking of the high- and low-resolution aerial images' lossy compression using the selected alternatives as 1 (A<sup>1</sup> )—JPEG2000, 25:1; 2 (A<sup>2</sup> )—ECW, 25:1; 3 (A<sup>3</sup> )—JPEG, 25:1; 4 (A<sup>4</sup> )—JPEG2000, 50:1; 5 (A<sup>5</sup> )—ECW, 50:1; 6 (A<sup>6</sup> )—JPEG, 50:1; 7 (A<sup>7</sup> )—JPEG2000, 75:1; 8 (A<sup>8</sup> )—ECW, 75:1; 9 (A<sup>9</sup> )—JPEG, 75:1; 10 (A10)—JPEG2000, 100:1; 11 (A11)—ECW, 100:1; 12 (A12)—JPEG, 100:1: (**a**) "img1" and its reduced version "img4"; (**b**) "img2" and its reduced version "img5"; (**c**) "img3" and its reduced version "img6".

As presented in Table 3 and Figure 7a–c graphs, the ranking of algorithms with different compression ratios according to the qualitative suitability for the high-resolution images "img1" and "img2" do not coincide. The "img3" ranking differs more from the first two because its content has more features sensitive to the lossy compression, such as the different types of textures, many small regions of different colors and intensities. The best quality presents JPEG2000 25:1 compression for all high-resolution images (1st place in Table 3, row 1), and the worst—JPEG 100:1 (15th place in Table 3, row 12). The JPEG2000 algorithm maintains better image quality than ECW and JPEG at compression ratios 50:1, 75:1, 100:1 (Table 3, JPEG2000 alternatives at 1st, 4th, 7th, 10th rows) too. Considering the threshold alternative *A*<sup>13</sup> for the JPEG2000 algorithm (Table 3, 13th row), a visually acceptable lossy compression for "img1" and "img2" was ranked above 6th place and for "img3" above 7th place. This corresponds to JPEG2000 compression lower than 100:1 for "img1" (Figure 8a) and lower than 75:1 for "img2" and "img3" (Figure 8e,f). ECW and JPEG algorithms were ranked worse than JPE2000 at all compression ratios. At lower compression ratios 25:1, 50:1, the JPEG algorithm (Table 3, JPEG alternatives at 3rd, 6th rows) was ranked higher than the ECW algorithm for "img1" and "img2". However, for "img3" can be seen the opposite tendency. At higher compression ratios 75:1, 100:1, the JPEG algorithm (Table 3, JPEG alternatives at 9th, 12th rows) was ranked worse than the ECW algorithm for "img1" and "img3". For "img2", JPEG 75:1 was ranked higher than ECW 75:1. Considering the threshold alternative *A*<sup>15</sup> for the JPEG algorithm (Table 3, 15th row), a visually acceptable lossy compression for "img1" was ranked above 9th place, for "img2" above 3rd place, and for "img3" above 6th place. This corresponds to JPEG compression lower than 75:1 for "img1" (near to 50:1 and less, Figure 8a), lower than 50:1 for "img2" and "img3" (near to 25:1 and less Figure 8e,f). The ECW compression rating is presented in 2nd, 5th, 8th, 11th rows of Table 3. At lower compression ratios 25:1, 50:1, the ECW algorithm was rated worse than the JPEG algorithm for "img1" and "img2", but at very high—100:1—compression ratios was rated higher than JPEG2000. Considering the threshold alternative *A*14 for the ECW algorithm (Table 3, 14th row), a visually acceptable lossy compression for "img1" was ranked above 11th place, for "img2" above 12th place, and for "img3" above 3rd place. This corresponds to ECW compression lower than 75:1 for "img1" (near to 50:1 and less, Figure 8a), and lower than 50:1 for "img2" and "img3" (near to 25:1 and less, Figure 8e,f).

**Figure 8.** Qualitative ranking of lossy compression algorithms with selected compression ratios solving the full and partial tasks for aerial images: (**a**) "img1"—by all the selected qualitative parameters (**b**) "img1"—by the texture quality; (**c**) "img1"—by the color quality; (**d**) "img1"—by the general quality metrics; (**e**) "img2"—by the all selected qualitative parameters; (**f**) "img3"—by the all selected qualitative parameters; (**g**) "img4"—by the all selected qualitative parameters; (**h**) "img5"—by the all selected qualitative parameters; (**i**) "img6"—by the all selected qualitative parameters; (**j**) legends for marking the compression algorithms for each image; (**k**) legends for marking the thresholds of compression quality of separate algorithms for each image.

A similar ranking tendency is observed for the corresponding low-resolution images "img4", "img5", and "img6" (Figure 8), but the changes of images' content due to the reduced resolution made the influence on the rating of lossy compression. The best quality presents JPEG2000 25:1 compression for all low-resolution images (1st place–Table 3, row 1), and the worst—JPEG 100:1 (15th place—Table 3, row 12). The JPEG2000 algorithm maintains better quality than ECW and JPEG at compression ratios 50:1 and 75:1 for "img4" and "img5", but at 100:1 for "img5" is superior ECW compression (Table 3, JPEG2000 alternatives at 4th, 7th, 10th rows). ECW compression at compression ratios 50:1, 75:1, 100:1 is superior to JPEG2000 compression for "img6" too. Considering the threshold alternative *A*<sup>13</sup> for the JPEG2000 algorithm, a visually acceptable lossy compression for "img4" was ranked above 7th place, for "img5" above 4th place, and "img6" above 6th place. This corresponds to JPEG2000 compression lower than 75:1 for "img4" and "img5" (near to 50:1 and less, Figure 8g,h), and lower than 50:1 for "img6". At higher compression ratios 75:1, 100:1, the ECW algorithm was ranked higher than the JPEG for the selected low-resolution images, but at low—25:1—compression ratios was ranked worse than JPEG for "img4" and "img5". Considering the threshold alternative *A*<sup>14</sup> for the ECW algorithm, a visually acceptable lossy compression for "img4" was ranked above 4th place, for "img5" above 9th place, and "img6" above 3rd place. This corresponds to ECW compression lower than 50:1 for "img4", "img5," and "img6" (near to 25:1 and less, Figure 8g–i). A visually acceptable JPEG lossy compression for was ranked by *A*15 alternative for "img4" above 5th place, for "img5" above 6th place, and "img6" above 5th place. This corresponds to JPEG compression lower than 50:1 for "img4", "img5," and "img6" (for all images near to 25:1 and less, Figure 8g–i).

The effect of lossy compression on the image content can be evaluated more precisely by the set of qualitative parameters and by using the parameters of the texture, color, and IQA, different subtasks can be solved: the same approach can be used to assess the texture, color, and general quality after the image lossy compression. Figure 8 shows the qualitative suitability of JPEG2000, ECW, JPEG compression for "img1" solving the full (Figure 8a,e–i) and partial tasks (Figure 8b–d)). Figure 8 shows that the JPEG2000 lossy compression is superior to the lossy ECW and JPEG compression in texture (b), color features (c), and by IQA (d). The JPEG compression provides similar image quality to JPEG2000 in texture features only at low compression ratios. JPEG has a significant effect on color, except at low compression ratios. The ECW compression at high compression ratios negatively affects texture but has a low impact on color. By IQA, the JPEG and ECW compression have a similar effect on the "img1" content.
