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Lecture 4: Transforms (98)

(Seed for discussion) This picture is a great example that ties two concepts that we have learned; transformation and aliasing! We will come back to this in a few lectures, but there is a lot happening in this scene; for instance, power line cables disappear (or invisible) as they get closer to the horizon. What observations would you make from this image, in terms of the relationship between resolution and distance? What technique would you use to avoid aliasing? Does the same aliasing persist in other transformations or unique to perspective transform?


As we look farther into the distance in this photo, it seems like the road and poles are getting blurrier, and also the cables, yellow paint, and wire fences are becoming harder and harder to see. My guess is that the culprit for both of these inaccuracies are due to each pixel needing to represent more area closer to the horizon. So if we are supersampling, for example, as the pixels represent a larger amount of space, the wires, yellow paint and cables become a more negligible part of the pixel, leading to these colors being less sampled and ultimately averaged out. The same goes for the words on the signs, for example: they are too small, leading to these details getting blurred. There is also some aliasing on the signs, most notably on the signs. This is likely for a very similar reason.


Intuitively the farther away objects in an image have less resolution than nearby objects. When objects are far away they are much smaller which translates to fewer pixels representing them. This can cause aliasing like invisible powerlines because small, distant objects like that would correspond to high frequencies with rapid color changes around the object. This is the same phenomenon as other kinds of image aliasing such as jaggies so it is not unique to perspective transform.


Moving closer to the camera, objects appear of higher resolution that objects that are farther in the distance. This likely happens due to the fact that the perspective of this image depicts the end of the road as farther in the distance, and thus the pixels closer to the end of the road/horizon need to take care of / represent more image than closer to the road. As a result, if we zoom into the distance, things like aliasing or jaggies occur due to the higher frequencies that exist

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