I'm enjoying this, thanks for investigating it further!
>"Note that AC is just a number (not a ratio), and this makes the ESC sensitive to file size. As we’ll see in future posts, I’m not entirely sure the ESC value turns out to meaningful because it varies widely with file size even when dealing with the same image."
How much variation are you seeing? I did notice there's a fair deal of variation at lower resolution, but as resolution increases it seems to level off gradually. Which makes sense because for a simple image (eg the French flag), the AC should stabilise/converge with increased resolution, and SS should tend towards 1. Although I'm not sure exactly how EF should behave...
SS does increase with image size (for the same image) while EF tends to decrease. ESC, of course, grows a lot — very roughly about half the file size. I'll be getting into this in a lot of detail in future posts.
For now, here are some figures. In all cases the original camera image was 4032x3024 and resized in an image editor to 2400x1800, 1200x900, and 400x300 versions. I'm using BMP images, so the file sizes at each resolution are identical among different images: 36,578,358 bytes, 12,960,054 bytes, 3,240,054, and 360,054 bytes respectively.
In the image of Bentley and going upwards in image size, the SS is 0.26, 0.36, 0.43, and 0.50. The EF is 1.82, 1.74, 1.71, and 1.70. The ESC is 127,237, 1,303,600, 5,424,765, and 15,473,620.
In the most non-compressible case, the image of those trees in the park, the SS is 0.08, 0.06, 0.06, and 0.09. The EF is 2.55, 2.55, 2.44, and 2.25. The ESC is 65,920, 476,601, 1,868,048, 7,136,494.
It seems the complex image has a lower ESC; roughly half that of the Bentley image, although the differences aren't consistent: 52%, 37%, 34%, and 46% respectively. And I'm not sure what to make of the ESC growing from 127,237 to 15,473,620 (in the Bentley image case) or from 65,920 to 7,136,494 in the trees image case.
Text files also vary. Three sources I used, Hamlet, Romeo & Juliet, and Macbeth, weigh in at 188,602 bytes, 149,102 bytes, and 109,288 bytes. They all have SS values of 0.63, which is about what most text is. They also all have an EF value of 2.43, again typical of text. But their ESC values are 106,902, 84,334, and 62,271, respectively. I think it differs so much because it's sensitive to file size. The SS and EF values seem to track something, but I'm not sure what ESC is telling me.
Ah OK, interesting. I think if you're looking at a high resolution image, the measure should be considered as working correctly if ESC goes up as the resolution goes up, since it is dealing with a genuinely more complex subject (a higher resolution image). It's only if the increased resolution does not add any more detail (eg with the flag) that we should hope for ESC to remain constant.
I also set up "normalised" ESC to help compare across resolution sizes, which divides the ESC by V(0), and manages to remove most of the variance. You might find that value/formula preferable or more insightful?
Yeah, that's pretty much what I've been figuring, a larger image has more detail, but I'm not clear on what it's telling me about the image or text content. SS is a nice measure on compressibility, and EF definitely seems sensitive to content, but I just haven't figured out what ESC tells me yet. Mostly because I've been more focused on SS and EF.
As I get more into analyzing ESC, I'll give that normalization idea a look. It might be interesting also to consider what we get with just SS×EF, since they're both normalized already and seem to carry interesting information.
I'm enjoying this, thanks for investigating it further!
>"Note that AC is just a number (not a ratio), and this makes the ESC sensitive to file size. As we’ll see in future posts, I’m not entirely sure the ESC value turns out to meaningful because it varies widely with file size even when dealing with the same image."
How much variation are you seeing? I did notice there's a fair deal of variation at lower resolution, but as resolution increases it seems to level off gradually. Which makes sense because for a simple image (eg the French flag), the AC should stabilise/converge with increased resolution, and SS should tend towards 1. Although I'm not sure exactly how EF should behave...
SS does increase with image size (for the same image) while EF tends to decrease. ESC, of course, grows a lot — very roughly about half the file size. I'll be getting into this in a lot of detail in future posts.
For now, here are some figures. In all cases the original camera image was 4032x3024 and resized in an image editor to 2400x1800, 1200x900, and 400x300 versions. I'm using BMP images, so the file sizes at each resolution are identical among different images: 36,578,358 bytes, 12,960,054 bytes, 3,240,054, and 360,054 bytes respectively.
In the image of Bentley and going upwards in image size, the SS is 0.26, 0.36, 0.43, and 0.50. The EF is 1.82, 1.74, 1.71, and 1.70. The ESC is 127,237, 1,303,600, 5,424,765, and 15,473,620.
In the most non-compressible case, the image of those trees in the park, the SS is 0.08, 0.06, 0.06, and 0.09. The EF is 2.55, 2.55, 2.44, and 2.25. The ESC is 65,920, 476,601, 1,868,048, 7,136,494.
It seems the complex image has a lower ESC; roughly half that of the Bentley image, although the differences aren't consistent: 52%, 37%, 34%, and 46% respectively. And I'm not sure what to make of the ESC growing from 127,237 to 15,473,620 (in the Bentley image case) or from 65,920 to 7,136,494 in the trees image case.
Text files also vary. Three sources I used, Hamlet, Romeo & Juliet, and Macbeth, weigh in at 188,602 bytes, 149,102 bytes, and 109,288 bytes. They all have SS values of 0.63, which is about what most text is. They also all have an EF value of 2.43, again typical of text. But their ESC values are 106,902, 84,334, and 62,271, respectively. I think it differs so much because it's sensitive to file size. The SS and EF values seem to track something, but I'm not sure what ESC is telling me.
Ah OK, interesting. I think if you're looking at a high resolution image, the measure should be considered as working correctly if ESC goes up as the resolution goes up, since it is dealing with a genuinely more complex subject (a higher resolution image). It's only if the increased resolution does not add any more detail (eg with the flag) that we should hope for ESC to remain constant.
I also set up "normalised" ESC to help compare across resolution sizes, which divides the ESC by V(0), and manages to remove most of the variance. You might find that value/formula preferable or more insightful?
Yeah, that's pretty much what I've been figuring, a larger image has more detail, but I'm not clear on what it's telling me about the image or text content. SS is a nice measure on compressibility, and EF definitely seems sensitive to content, but I just haven't figured out what ESC tells me yet. Mostly because I've been more focused on SS and EF.
As I get more into analyzing ESC, I'll give that normalization idea a look. It might be interesting also to consider what we get with just SS×EF, since they're both normalized already and seem to carry interesting information.