Determining Focal Length Increments for Infinite Zoom

[Lin Evans]

One of the issues which has become apparent when playing with the infinite zoom concept is how to match ending zoom points with beginning zoom points on following slides. That has pretty well been worked out essentially by temporarily adding the next desired slide to the existing slide as an object, setting each opacity to less than 100% and manually/visually matching at ending keypoint for first slide. Then either copy numbers to insert in following slide or copy slide object, delete following slide and paste copied slide. That works well for the match and with perspective zoom, careful color match, display time match, etc., an excellent continuous zoom can be accomplished. But another problem presents itself and that is how to correctly determine the proper focal length increments for the original captures so as to:

1. Prevent pixelation by too deep zoom

2. Have sufficient overlap so as to allow a match without a black border on the zoomed out image

There are probably more scientific and better ways to accomplish this, but my head is beginning to hurt from trying to decipher the variables so this is how I approach it.

I take one of my original image which has not been altered and bring it into PTE. I've discovered that with my dSLR's which have a different aspect ratio than a 4:3 computer monitor I need a zoom of 112 to just fill the screen vertically without a black border. That's my starting point.

Next I open the same image in Irfanview (to see it at 100% size without any resample) and use both Irfanview and PTE in the windowed mode. I increase the zoom on the PTE file until a measured object in the image just matches the measurement in Irfanview of the 100% image. In my case it turns out that the zoom is exactly 258. This figure will be different for different cameras depending on the pixel dimensions of your original file. In many, if not most cases, this will be a larger number. I'm using a dSLR which produces a 4.46 megapixel file with a 14 megapixel sensor, so my numbers don't reflect the norms.

The point is, that I can then use this figure (258) in my case as a percentage of increment for focal lengths necessary to match maximum zoom in on frame "A" to matching maximum zoom out on frame "B". So if I take an image at 100mm then I can safely jump to 258mm for the second image then to as much as 666mm on the third frame, etc. I can always go "less" in terms of increments, but if I go more then I must either exceed 100% unpixelated zoom on my first image or have a black border on the matching image from the next slide.

This is just a quick "non-mathematical" method of determining which increments you can use with your own cameras. Use a 100% sized image to measure some feature, match that feature in zoom with PTE and observe the zoom number. Use this number as a percentage of focal length safe to increment for your sequence. So if your own number turns out to be 432 then that's 4.32 times the lower focal length as a "step" or "increment" for the next frame. If your number is 347 then 3.47 times the lower focal length, etc.

Lin

[cjdnzl]

Hello Lin,

An interesting concept. Going by your 14 MP reference to your image size, according to my math that's about a 3055 x 4582 pixel image, assuming a 1:1.5 aspect ratio. (what camera is that?)

Now, if you are setting up your show image size to, say, 1024 x 768, then for your camera image at 3055 pixels high, you can afford a zoom of 3055/768, = 3.9779 times, and at that zoom ratio, your original image will be at 100% on the computer screen. The width is always going to get cropped, so it can be ignored, unless you are doing 16:9 ratio shows, when the width becomes the calculated parameter.

If you step your focal length increments at 3.9779:1, theoretically the images should match when the first is at 397.79 in the PTE zoom 'counter', and the second is at 100.00 in PTE, i.e. un-zoomed.

This result depends, of course, on how accurately one can set the focal length of the taking lens, and in practice that is probably impossible, so the problem devolves into finding the size ratio between two images taken with different focal length lenses.

Therefore, this problem boils down to measuring two images and finding the size ratio, which is effectively what you are doing now with Irfanview.

Importing both images into Photoshop will allow you to use the measuring tool, but whether this would be any closer than you are already getting would have to be experimented with.

I think I'll have a play in PS.

Colin

[cjdnzl]

Further to the infinite zoom attempts, I have seen another problem. The zoom speed in PTE looks to be linear with image area, i.e. as the image zooms in, the rate of linear zoom slows down. With large zoom ratios this effect causes noticeable 'jumps' in the apparent zoom rate.

Perhaps the zoom ratio will have to be restricted, say to about 1.5:1 to minimize this effect. Maybe an increasingly cropped series of the same image in Photoshop would be called for, each with, say a zoom ratio of 1.414:1, so it would take two images to get a ratio of 2:1, and so on.

If a total zoom ratio of, say, 128:1 was contemplated, then one would need 14 images to achieve it, each zoomed in 1.414 times and re-cropped to just fit the screen. (1.414^14 =128 approx.)

Note to Igor: Is there any possibility that the linear zoom could be made to be a constant size increase rather than constant area? As it is now, the zoom slows as the image gets bigger, and when zooming out, the zoom speed increases as the image gets smaller.

Colin

[Lin Evans]

Hello Lin,

An interesting concept. Going by your 14 MP reference to your image size, according to my math that's about a 3055 x 4582 pixel image, assuming a 1:1.5 aspect ratio. (what camera is that?)

Hi Colin,

I have a large collection of digital cameras (over 30) but the one which I use for macro and detail work is a bit different than conventional digital cameras. It's a Sigma SD14 which has a rather unique Foveon sensor which has 14 million photosites however not arranged in a conventional two dimensional array but rather a three dimensional array so that the triad of RGB values are directly measured simultaneously for each pixel location. This then produces a digital file of (4.64 megapixels) 2640x1760 pixels. The file size is much smaller than a conventional CFA sensor containing the same number of photo detecting pixels, but the optical resolution for black and white is about equivalent to a 10 megapixel conventional camera while the color resolution is about that of an 16 megapixel conventional sensor. It has a "crop factor" viz 35mm of 1.7x.

The 100% image is reached at a PTE zoom value of 258, but because of the optical resolution being much higher than a corresponding 4.6 and the pixel level sharpness superb, I can actually zoom in much further and still avoid pixelation.

Now, if you are setting up your show image size to, say, 1024 x 768, then for your camera image at 3055 pixels high, you can afford a zoom of 3055/768, = 3.9779 times, and at that zoom ratio, your original image will be at 100% on the computer screen. The width is always going to get cropped, so it can be ignored, unless you are doing 16:9 ratio shows, when the width becomes the calculated parameter.

Yes, that works well for a conventional display (4:3) with those parameters and as you imply, one could also use the horizontal pixel count in the same manner.

If you step your focal length increments at 3.9779:1, theoretically the images should match when the first is at 397.79 in the PTE zoom 'counter', and the second is at 100.00 in PTE, i.e. un-zoomed.

Yes - and easy enough to not go too far on the focal length zoom so as to allow for some overlap to facilitate keeping black margins out of the frame when zooming back on the secondary image to match zoom in on the first.

This result depends, of course, on how accurately one can set the focal length of the taking lens, and in practice that is probably impossible, so the problem devolves into finding the size ratio between two images taken with different focal length lenses.

It's not easy without taking a few extra frames and checking the EXIF (assuming the lens reports the focal length used) or using the "rough" calibration on the lens itself.

Therefore, this problem boils down to measuring two images and finding the size ratio, which is effectively what you are doing now with Irfanview.

Yes - crude but effective.

Importing both images into Photoshop will allow you to use the measuring tool, but whether this would be any closer than you are already getting would have to be experimented with.

Probably more accurate, but would take a bit longer.

I think I'll have a play in PS.

Colin

[Lin Evans]

Hi Colin,

That's the nice thing about the new "non-linear" zoom and "perspective correction" in PTE 5. You can tailor the zoom to any curve desired so can control the apparent speed with near infinite precision. It's actually the "transition" points where the difficulty arises. I'm hoping for a separate "zoom-in" and "zoom-out" control in a future version to facilitate making an apparent continuous zoom.

Actually when I first posted, I wasn't too concerned (still not) about the continuity of the zoom as appearing to zoom a single huge image at constant speed so much as the ability to string relatively seamless matched images together to go from extreme wide angle to extreme macro on the same subject. My original intent was to be able to show closeup detail in areas from panoramas such as the Cliff Palace sample I posted. I would like to be able to shoot the initial frames for the stitched panorama then connect a series of longer focal length lenses to get photos which could be seamlessly dropped in at desired places on the slideshow to show extreme detail.

Fortunately I have lenses going to optical focal lengths of as much as 1600mm (with 2x tele converter) and telescopes which I routinely use with various digicams to shoot at focal lengths of up to 6000mm with good light. I can envision, for example, being able to literally show the whiskers on a mouse or pika setting on an adobe brick at Cliff Palace in one of the rooms, and this done from the zoom off the stitched panorama. Admittedly, it's more than a bit of a grandiose experiment, but I think it can be done.

On the topic of using the same image in stages - yes, actually I did that in my Kachina example. I interpolated a very good, well focused macro with Genuine Fractals (for edge sharpness) to get better than 1:1 on the closeups. The original macro was used then the interpolated and cropped version then back to the original in the slideshow. That's one of the very useful things about the SD14 - the ability to enlarge without serious loss of quality. I had several photos taken with it displayed at PMA in Los Vegas this year which were larger than A0 print size which turned out very well.

Best regards,

Lin

Further to the infinite zoom attempts, I have seen another problem. The zoom speed in PTE looks to be linear with image area, i.e. as the image zooms in, the rate of linear zoom slows down. With large zoom ratios this effect causes noticeable 'jumps' in the apparent zoom rate.

Perhaps the zoom ratio will have to be restricted, say to about 1.5:1 to minimize this effect. Maybe an increasingly cropped series of the same image in Photoshop would be called for, each with, say a zoom ratio of 1.414:1, so it would take two images to get a ratio of 2:1, and so on.

If a total zoom ratio of, say, 128:1 was contemplated, then one would need 14 images to achieve it, each zoomed in 1.414 times and re-cropped to just fit the screen. (1.414^14 =128 approx.)

Note to Igor: Is there any possibility that the linear zoom could be made to be a constant size increase rather than constant area? As it is now, the zoom slows as the image gets bigger, and when zooming out, the zoom speed increases as the image gets smaller.

Colin