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Old May 30, 2003, 11:14 AM   #31
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Quote:
Originally Posted by Grand Dizzy
... Everyone seems to be in agreement that cropping an image down is not the same thing as zooming.
Not the same as "zooming" (silly word), but the difference is subtle. The field of view that comes from cropping can be exactly the same as shooting with a longer lens, but at lower resolution. My objection to your earlier post was the use of numbers. It is the square root of the ratio of pixel count that determines the effective "zoom".

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Originally Posted by Grand Dizzy
For this to be true; for these to produce two different photos, then cameras must give less detail at higher resolutions.
As many folks have pointed out, that statement is complete nonsense akin to saying that to be tall you must be short.

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Originally Posted by Grand Dizzy
I have always assumed that if I use twice the number of pixels to take a photo, then I should have twice as much detail.
Wrong - detail is linear a linear measurement while pixel count is a surface (area) measurement. Detail increases as the square root of pixel count - not linear.

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Originally Posted by Grand Dizzy
So I should be able to zoom out and get twice as much in the photo, and still make out exactly the same details as I could see with half the number of pixels. Because the original area of the photo is still covered by as many pixels as it used to be.

If I can't see that detail any more, then the camera must be giving me less detail at higher resolutions. And therefore having more pixels is pointless.
And do it again, and again, and again, .... So you should be able to take the highest resolution with only one pixel. Can't you see the absurdity of that?


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Originally Posted by Grand Dizzy
If 4 megapixel cameras take exactly the same photo as 1 megapixel cameras (only with 4 times the number of pixels) then you may as well just take the photos at 1 megapixel setting and scale them up to 4 megapixels on the computer. That way you can store 4 times as many photos on the camera's memory.
And a 0.25 MPixel would do as well as 1 Mp. And a 0.0625 MPixel as well as a 0.25. And .... And a 1 Pixel camera would do as well as an infinite MPixel camera.


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Originally Posted by Grand Dizzy
If that isn't the case, then 4 megapixel photos do give 4 times more detail. And therefore you should be able to crop them down to a fourth of their size and still get the same level of detail as a 1 megapixel photo.
True if you by "a fourth of their size" you mean 1/4th of the area, or 1/2 of the linear size.

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Originally Posted by Grand Dizzy
And therefore zooming by cropping is perfectly acceptible.
True, but at lower resolution.
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Old May 30, 2003, 7:55 PM   #32
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Originally Posted by BillDrew
My objection to your earlier post was the use of numbers. It is the square root of the ratio of pixel count that determines the effective "zoom".
What's this square root business? Is it really relevant to zooming? If I crop a 4 megapixel image down to a 1 megapixel image then I have changed the size of the photo to a quarter of its original size. Therefore, I have performed a 4x zoom. Because the cropped area is now 4 times "bigger". Similarly, if I take a photo at 2272x1709 then its pixel count is 3871488. If I crop it down to 1280x960 (1228800 pixels) then the cropped area of the photo is now 3.150625 times "bigger". And if the original image was zoomed in at 3x zoom, then multiplying these two figures together you get a total zoom of 9.451875x.

I don't see how square roots come into it.

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Originally Posted by BillDrew
Quote:
Originally Posted by Grand Dizzy
For this to be true; for these to produce two different photos, then cameras must give less detail at higher resolutions.
As many folks have pointed out, that statement is complete nonsense akin to saying that to be tall you must be short.
It's not self-contradictory, as you imply. But I never actually believed it myself. It was only a hypothesis to explain how cropping an image could result in lower detail.

If you crop down a high res photo and the detail of the remaining area is not as good as a photo that was taken at that size originally, then it stands to reason that higher res photos are lower quality.

To put this into an example, imagine you take a 2 megapixel image of a man's face (zoomed in 2x). You then take a 4 megapixel image of the man's whole body (zoomed out) and crop down this photo down to 2 megapixels. So you now have two photos of the same thing - at the same resolution. Now, if the photo that was originally taken at the higher resolution doesn't look as sharp as the first photo, then clearly your higher resolution photo is lower quality. It's not contradictory, because higher resolution doesn't necessarily mean better image quality.

Scanners are a good example of this. Some scanners say that they scan at, say, 1200 dpi. But they actually just scan at 600dpi and interpolate the image up to 1200dpi. One could look at this in three ways...

1) One could say that both a 600dpi scan and a 1200dpi scan are identical, as they are effectively the same image (they would certainly look identical when viewed as a whole).

2) One could say that the higher resolution scan is "better quality" simpy because it has more pixels, and if both images were printed out at the same size, the higher res one would be less pixellated.

3) But personally I think the higher resolution scan is definitely lower quality. It has a lower ratio of detail to pixels. The pixels aren't doing their job of discerning individual points of colour information. And at least three quarters of the pixels are useless. Their only purpose is to blend one colour to another.

Most importantly though, in many cases scaling/interpolating an image to a higher resolution results in a lack of quality because the colour of all the pixels is recalculated, which often results in original detail being lost. When images are scaled up to an exact multiple of their original dimensions, then there is less chance of losing detail. but other than that, scaling/interpolating is usually a bad thing and reduces an image's quality.

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Originally Posted by BillDrew
Quote:
Originally Posted by Grand Dizzy
I have always assumed that if I use twice the number of pixels to take a photo, then I should have twice as much detail.
Wrong - detail is linear a linear measurement while pixel count is a surface (area) measurement. Detail increases as the square root of pixel count - not linear.
I don't agree with this. A photo is made up of pixels. The number of pixels determines the level of detail. Doubling the pixel count must double the detail, because you have twice your original amount of information. If I scale a 4 megapixel image down to a 1 megapixel image, I am quite clearly dealing with an image a quarter of the original size, because you could fit 4 of them in the original. It's a quarter of the original size, and has a quarter of the original detail.

If I have a 1 pixel image and I add a second pixel, have I not doubled its detail? If I add two more pixels have I not doubled its detail again? Therefore doubling 2 megapixels to 4 megapixels is doubling the detail. (It certainly is in my opinion, anyway.)
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Old May 30, 2003, 8:58 PM   #33
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Quote:
Originally Posted by Grand Dizzy
If I have a 1 pixel image and I add a second pixel, have I not doubled its detail? If I add two more pixels have I not doubled its detail again? Therefore doubling 2 megapixels to 4 megapixels is doubling the detail. (It certainly is in my opinion, anyway.)
You are free to define things the way you want as well as living under the bridge with the other trolls.
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Old May 30, 2003, 9:07 PM   #34
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Originally Posted by Grand Dizzy
Can anyone please explain to me how cropping an image is not the same as zooming. I realise the resolution will be lower (duh!) but surely it will be exactly the same photo as if you had zoomed in.
Lets put this in simpler words.

When you crop, YOU are doing the zooming and loosing information in the process. The cropped image has less pixels than the original.

When the camera does the zooming, you still get the same amount of pixels but the subject looks closer. You have more information in the resulting image than the cropped version.

More information means (in theory) a crisper printed picture.

I said "in theory" because I recently printed some pictures in a photo lab at 6x4. One of them was of a group of people and the person that took the picture left way too much space on the sides instead of taking up the whole picture with the group. I cropped that one in my computer to about 1/4 of the original size to make the group look closer (exactly what you do - in effect, a 2x zoom). When I went back to the photo-lab to print that picture at the same size as before, it doesn't look any better or worse than the original picture, just closer. But if I go and print it a 11x14 the difference might be noticeable.

At the end, it all depends.

But cropping is definitely NOT THE SAME as optical zoom done by the camera.
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Old May 30, 2003, 11:06 PM   #35
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Grand Dizzy

First off, I just want to be clear. Iíve seen you answer some other questions in very intelligent ways. Iím keeping at this so that we can get to the bottom of it (for the records) and so we donít annoy you enough to drive you away. Personally, Iíd rather you stayed. Forums like these only thrive when people with knowledge share with others that donít have it. I hope we arenít bothering more than a normal disagreement between people does.

This is where the square root comes into it. BillDrew is talking about how enlarging the x&y of sensor effects the number of pixels. You are talking about raw numbers of pixels. So you are both right. Here is an illustration of what Bill is saying:
Take the sensor of the 3MP Nikon 995: 2048 x 1536 = 3145728 pixels. Now, increase the x & y by 1/3 each. You might thing would get you 4MPÖ itís 3MP enlarged by 1/3, right? But you don't. If you increase the x&y by 1/3 each you get 2730x2048 = 5591040 pixels. A lot more than 4MP. This is because as you enlarge the sensor, the MP of the camera does not grow linearly. I donít know what the equation is that can calculate MP from how much you enlarge the x&y of a sensor Ö but there is one and it isnít a direct linear calculation.

You never commented on either kcembís or my posts. Did you read them? I made points and asked questions which you didnít answer or touch on. Instead of going on very long, Iím going to just ask a few questions and hope they are answered. I want to set the foundation for clearing this up.

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Originally Posted by Grand Dizzy
And why can't I consider my camera to have 9.5x zoom capability at 1280x960? Surely the objects in the photo appear 9.5 times bigger than they would appear had I not zoomed in 3x and cropped the image to just under a third its original size.
You only say ďcrop the imageĒ. Do you really mean this? You do not enlarge the image (through some form of interpolation) to get back to the same number of pixels as the uncropped image? This matters a lot. One way gives you fewer pixels than the other.

Mike_PEAT described how cropping just looses data. Did you agree with his description of how to simulate a crop physically and comparing it with what a zoom does?

Quote:
Originally Posted by Grand Dizzy
Everyone seems to be in agreement that cropping an image down is not the same thing as zooming.
Does everyone include you? I assume not, but I want to be sure/clear. When you "zoom" your camera, you always produce a picture of a given MP. If you crop (and only crop) a picture, you loose data. You do not have the same size picture. It isnít fare to say that if I crop, I have the same as a longer zoomÖ you have a smaller picture with less data so they are not the same! Of course, having less data only matters if your display device can show all the data you had originally, but that is what kcemb got into (and you didnít comment on.)

Quote:
Originally Posted by Grand Dizzy
Scanners are a good example of this. Some scanners say that they scan at, say, 1200 dpi. But they actually just scan at 600dpi and interpolate the image up to 1200dpi. One could look at this in three ways...
This is the first time you have ever mentioned interpolation. You changed the ground rules between ďthe scanner exampleĒ and ďthe camera and cropĒ example. Please do not do this when forming arguments. Your scanner example is an interesting one, and Iíll talk about that if you want. But it's not the same situation as everything else that has been discussed.
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Old May 31, 2003, 7:09 AM   #36
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Default The square root business

Let me try to sort out the square root business.
First you need to understand the numbers that are used when referring to mpixels and zoom ratio.
Zoom ratio is not a pixel count ratio nor is it an area ratio. It is a linear measurement.
An item in a picture which is 2 foot long will appear to be 6ft long if a 3x zoom is applied. It is a linear measurement not an area measurement. Please stop and think about it. You need to understand this as it is fairly fundamental!

If an object is 2x2, [area = 4] any units will do, and you perform a 4x zoom, the object becomes 8x8, [area = 64] You will see that the area is 16x greater than before the zoom. In other words, the square of the zoom ratio. Do it in reverse and this is where the square root comes in. A camera that has 2 mpixels compared to another with only 1 megapixels, does not have a picture twice as big, even though the pixel count is double. If you work it out, in a square format to make it easier, the 1 megapixel frame would be 1000 pixels x 1000 pixels. But the 2 megapixels frame would be 1414x1414, giving 2,000,000 pixels. You will see that the linear size of the image has increased by a factor of 1.414, ie the square root of the area ratio.

Somewhere in this long posting the original poster claimed going from 1 mpixel to 4 mpixel is a 4x zoom because it has 4x the area. This is simply not the way zoom is measured as explained above. That would be called a 2x zoom, because the image has changed linearly by 2x. Clearly the poster does not understand this to be the case, but he needs to, because that is the standard way a zoom is defined.

Now let me try simply to sort out the cropping/zooming issue, bearing in mind that it may be irrelevant to the original poster who only looks at monitor images anyway.

When you zoom optically, ie with the lens changing its focal length, if your camera has1600x1200 pixels, then you always have 1600x1200=1.92 million little dots of information available to you to print or show on a monitor, whatever the amount of optical zoom you have used.

If you do not zoom, but take the same picture at wide angle then crop a 1600x1200 image to get the same picture as the optically zoomed image, so that the result is a picture of 800x600 pixels, or items of information, then that is all the information you have to deal with.

The picture resulting from optically zooming, has1600x1200 pieces of information. the cropped image has only 800x600 pieces. Almost whatever you do with that image, the results will be less "sharp" because there is just not the same amount of informatoion available.

If your monitor was only 800x600, the 2 pictures would look the same, but that is irrelevant. If you show the 800x600 picture on a 1024x768 monitor, the computer will fill in the gaps to enalrge the picture to the monitor size, and the picture will loose sharpness compared to a picture with the same number of pixels [or a greater number] as the monitor.

If you print the picture which is 800x600 as the result of cropping, the print will have less detail, ie be less "sharp" than the same scene resulting from zooming to a full 1600x1200, provided of course that the prints are the same size and big enough that loss of detail can become apparent. [Obviously a 12"x9" print will show loss of detail more readily than a 4"x3" print. That does not need an explanation I hope.]

And do not be misled by software that resizes an 800x600 image to say 1600x1200. The result will look acceptable, even very good perhaps. But the software has had to fill-in missing pixels by guessing from nearby pixels, what might have been there if there had been more pixels in the first place. There are ways of guessing that are more clever than others, but it is still guessing and inventing information which is simply not there. And the result is a less "sharp" picture.

[For the pedants, yes, I know about the various algorithms that Photoshop uses, and how good the results are, but this is my attempt at a simple explanation of what I always thought was totally obvious.]

I shall now bow out of this posting. Much has been done to explain what many take as so obvious as to not need explaining, and any more would be prolonging the agony.
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Old Jun 1, 2003, 1:56 PM   #37
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kcemb said "If an object is 2x2, [area = 4] any units will do, and you perform a 4x zoom, the object becomes 8x8, [area = 64]"

I always thought that zooming and enlarging were two different things?, different ratios? if I zoom in on something 4x does it enlarge it 4x?

thanks
Steve :?:
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Old Jun 1, 2003, 2:46 PM   #38
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Default Zoom

If you zoom 4x, any object in the frame will become 4x wider and 4x taller ie 4x in each of its 2 dimensions. So the area it occupies is 4x4=16 times what it was. Using expressions like 4x "bigger" leads to confusion.
Prove it to yourself by looking at a garden gate through the finder at full wide angle, note roughly how big the gate looks, then zoom the max you camera allows. If you have a 3x zoom, the gate will be 3x wider and 3x taller.
You dont have to trust me, just do it.
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Old Jun 1, 2003, 4:20 PM   #39
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I think you guys are trying to confuse a newbie. If I want to print a full image 4X6, it will have 300 pixels per inch, (just as an example). If I then blow the picture up to 8X12, it will have 150 pixels per inch. If I then crop a section of this enlargement to 4X6, it will still have 150 pixels per inch. The question of sharpness then becomes at what number of pixels per inch do I start noticing a degradation in image quality. This will, of course, be a function of how I print the image. But using the same printing method for all prints, the number of "dots" per inch determine what you see. So an optical zoom of 10X should give a sharper image than a 10X digital enlargement.
Am I right?

Thanx,

Ron
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Old Jun 1, 2003, 4:29 PM   #40
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What's a pixel? :lol:
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