🚀 go-pugleaf

sjreeves@eng.auburn.edu (Stan Reeves) writes:

>In article <yi.714929332@fife.ecn.purdue.edu> yi@fife.ecn.purdue.edu (Juneho Yi) writes:
>>sjreeves@eng.auburn.edu (Stan Reeves) writes:

>[ stuff on objective measures for restoration quality ]

>>>I'm assuming that the original poster is interested in objective measures
>>>that have some correlation to the assessment a human observer would make.
>>>Does this measure have any relationship to subjective evaluation?  What is
>>>the point of normalizing with respect to surface area?
>>
>>By normalizing the volume by the surface area, the value of the measure 
>>can be compared for different size of images.

>This is usually done simply by dividing by the number of pixels in the
>image.  Is there any advantage of dividing by surface area?  By surface
>area, are you thinking of an image as a 2-D contour map?  If you just
>mean height*width, then that's the same as dividing by the number of
>pixels.

The problem I am talking about is image reconstruction of the graph surface
form, z = z(x,y). Let's say we have two same surfaces z1, z2 and that z1 
is rotated about x or y axis. Then the projected areas of z1 and z2 onto x-y
plane are not the same any more. Hoever, the surface areas of z1 and z2 are
still invariant to the rotation.

>Also, what about "volume"?  This sounds like mean absolute error to me.

No, I compute approximate volume between the reconstructed surface and the
original noiseless surface to see how close the surface is reconstruted 
to the original surface.

>>The Mean-Square error is kinda L2 metric.
>>Apparently, if MSE is used as a measure, where the slope is high,
>>the difference value is emphasized more than in flat regions.
>>I am saying that MSE measure is ** not invariant ** w.r.t. a coordinate system.
>>The original poster was looking for methods to compare various algorithms on
>>image restoration, wasn`t it ?

>When you speak of a coordinate system, are you thinking of an image as a
>signal in two dimensions or are you thinking of each pixel as a dimension
>so that we have a signal in an MxN-dimensional vector space for an MxN 
>image?  If you mean the second, then MSE *is invariant* with respect to
>a coordinate transformation.  It also seems pretty clear that it's invariant
>in the sense of a 2-D coordinate transformation.  Can you clarify?

Of course, I am thinking of an image as a signal in two dimensions.

>--
>Stan Reeves
>Auburn University, Department of Electrical Engineering, Auburn, AL  36849
>INTERNET: sjreeves@eng.auburn.edu