[R] `level' definition in `computeContour3d' (misc3d package)
murdoch.duncan at gmail.com
Sat Nov 9 19:40:26 CET 2013
On 13-11-09 12:53 PM, j. van den hoff wrote:
> On Sat, 09 Nov 2013 18:18:23 +0100, Duncan Murdoch
> <murdoch.duncan at gmail.com> wrote:
>> On 13-11-09 11:57 AM, j. van den hoff wrote:
>>> On Sat, 09 Nov 2013 17:16:28 +0100, Duncan Murdoch
>>> <murdoch.duncan at gmail.com> wrote:
>>>> On 13-11-09 8:50 AM, j. van den hoff wrote:
>>>>> I'd very much appreciate some help here: I'm in the process of
>>>>> whether I can use `computeContour3d' to derive estimates of the
>>>>> area of a single closed isosurface (and prospectively the enclosed
>>>>> volume). getting the surface area from the list of triangles returned
>>>>> `computeContour3d' is straightforward but I've stumbled over the
>>>>> meaning of `level' here. looking into the package, ultimately the
>>>>> used in the namespace function `faceType' which reads:
>>>>> function (v, nx, ny, level, maxvol)
>>>>> if (level == maxvol)
>>>>> p <- v >= level
>>>>> else p <- v > level
>>>>> v[p] <- 1
>>>>> v[!p] <- 0
>>>>> v[-nx, -ny] + 2 * v[-1, -ny] + 4 * v[-1, -1] + 8 * v[-nx,
>>>>> my question: is the discrimination of the special case `level ==
>>>>> (or rather of everything else) really desirable? I would argue
>>>>> that always testing for `v >= level' would be better. if I feed data
>>>>> discrete values (e.g. integer-valued) defined
>>>>> on a coarse grid into `computeContour3d' it presently makes a big
>>>>> difference whether there is a single data point (e.g.) with a value
>>>>> than `level' or not. consider the 1D example:
>>>>> data1 <- c(0, 0, 1, 1, 1, 1, 1, 0, 0)
>>>>> data2 <- c(0, 0, 1, 2, 1, 1, 1, 0, 0)
>>>>> and level = 1
>>>>> this defines the isocontour `level = 1' to lie at pos 3 and 7 in for
>>>>> but as lying at pos 4 in data2. actually I would like (and expect) to
>>>>> the same isosurface for `data2' with this `level' setting. in short:
>>>>> meaning/definition of `level' changes depending on whether or not it
>>>>> equal to `maxvol'. this is neither stated in the manpage nor is this
>>>>> desirable in my view. but maybe I miss something here. any
>>>>> would be appreciated.
>>>> I don't see why you'd expect the same output from those vectors, but
>>>> since they aren't legal input to computeContour3d, maybe I don't know
>>>> what you mean by them. Could you put together a reproducible example
>>>> that shows bad contours?
>>> it's not "bad" contours, actually. my question only concerns the
>>> of `level' depending on whether `level = maxvol' or not.
>>> here is a real example:
>>> dim <- 21
>>> cnt <- (dim+1)/2
>>> wid1 <- 5
>>> wid2 <- 1
>>> rng1 <- (cnt-wid1):(cnt+wid1)
>>> rng2 <- (cnt-wid2):(cnt+wid2)
>>> v <- array(0, rep (dim, 3))
>>> #put 11x11x11 box of ones at center
>>> v[rng1, rng1, rng1] <- 1
>>> con1 <- computeContour3d(v, level = 1)
>>> dum <- readline("CR for next plot")
>>> #put an additional 3x3x3 box of twos at center
>>> v[rng2, rng2, rng2] <- 2
>>> con2 <- computeContour3d(v, level = 1)
>>> this first puts a 11x11x11 box one Ones at the center of the
>>> zero-initalized array and computes `con1' for `level=1'. in the 2. step
>>> it puts a further, 3x3x3 box of Twos at the center and computes the
>>> `level=1' contour again which this time does not delineate
>>> the box of Ones but lies somewhere between the two non-zero boxes since
>>> now the test in `faceType' is for `> level'. this is not immediately
>>> obvious from the plots (no scale) but obvious from looking at `con1' and
>>> `con2': the `con2' isosurface is shrunk by 3 voxels at each
>>> side relative to `con1' (so my initial mail was wrong here: `con2' does
>>> not "jump" to the next "discrete" isocontour but rather to
>>> a point about halfway between both plateaus ). I also (for my own
>>> at hand) computed the total surface area which is
>>> (not surprisingly...) 600 for `con1' and 64.87 for `con2'. so if one is
>>> interested in such surfaces (I am) this makes a big difference in such
>>> the present behavior is not "wrong" per se but I would much prefer if
>>> test where always for `>= level' (so that in the present example the
>>> resulting isosurface would in both cases delineate the box of Ones -- as
>>> is the case when using `level = 1-e-6' instead of `level=1').
>>> I believe the isosurface for a given value of `level' should have an
>>> unambiguous meaning independent of what the data further "inside" are
>>> looking like.
>> I think it does, but your data make the determination of its location
> I was imprecise: what I meant is: the isosurface should not change in my
> example between both cases.
>> The definition is the estimated location where the continuous field
>> sampled at v crosses level.
>> You have a field with a discontinuity (or two). You have whole volumes
>> of space where the field is equal to the level. The marching cubes
>> algorithm is designed to detect crossings, not solid regions.
>> For example, going back to one dimension, if your data looked like your
>> original vector
>> data1 <- c(0, 0, 1, 1, 1, 1, 1, 0, 0)
>> then it is ambiguous where it crosses 1: it could be at 3 and 7, or
>> there could be multiple crossings in that range. I believe the
>> analogous situation in misc3d would treat this as a crossing at 3 and 7.
> yes, it does that. and it is clear that due to your interpretation it
> about point 3.5 and 6.5 (?) for
> data2 <- c(0, 0, 1, 1, 2, 1, 1, 0, 0).
I don't think it does. I think it picks 4 and 6. In your 3d example,
the smaller cube runs from 9 to 13 in each coordinate (though it misses
the corners). You can see this if you plot it using the "rgl" engine,
then call rgl::decorate3d() to add axes.
> still, depending on application I would maintain that it can make (more)
> to keep the isosurface at 3,7 in this case.
That makes just as much sense, but not more. Anywhere from 3 to 4 is a
sensible left end, anywhere from 6 to 7 is fine for the right end.
> I believe the problem maybe is not so much "discrete vs. continuous" but
> whether there is
> a constant "plateau" in the data: even for the underlying continuous field
> it is a matter
> of convention, then, where to put the level=1 contour: at the first
> crossing, in the middle
> of the plateau, or at the second crossing. I understand `computeContour3d'
> essentially puts
> the contour in the middle of the plateau.
No, it doesn't. As you've seen, it handles plateaus inconsistently
depending on whether they are the max of the field or not. For the case
where it is an interior plateau, you get your contour at height
level+epsilon in an approximation to the field. For the max of the
field, you get level.
Try comparing the contour you get at level 1 with v and at level -1 with
-v. They are not the same.
> I do not want to claim present behavior is a bug. it just is not
> necessarily what
> is needed. an additional argument/flag to `computeContour3d', e.g., to
> select behaviour in this
> sort of "degenerate" cases (exhibiting strictly constant plateaus) would
> be great.
You can suggest this to the maintainer of the package (I am not author
or maintainer of it).
> from a purely practical point of view: as explained I want to get the
> "outer isosurface" of such
> preprocessed discretized data and quantify the surface area. the question
> here is "when do the data
> first cross the threshold" and that's where the present behaviour causes a
> problem for me.
You may need to write your own function for this.
> but anyway thanks for bothering. if it is deemed undesirable to change
> present behaviour (or to add
> a further flag for controling the behaviour of `level') I can fix it
> locally for my needs by
> just changing the test in `faceType' (or so I presume).
>> Duncan Murdoch
More information about the R-help