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Re: Converting a magnified image of a line to a single

• To: mathgroup at smc.vnet.net
• Subject: [mg130609] Re: Converting a magnified image of a line to a single
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 26 Apr 2013 04:23:56 -0400 (EDT)
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• References: <20130417063041.7376E6A61@smc.vnet.net>

trace = Import["http://www.d-a-v-e.org/images/Trace.jpg";]
b = ColorNegate@Binarize[trace];
b2 = SelectComponents[b, "Area", -1];
b3 = FillingTransform@b2;
dt = ImageAdjust@DistanceTransform@b3;
resultOut = ImageValuePositions[Image[WatershedComponents[dt], "Bit"], 0];
bsf1 = BSplineFunction[MovingAverage[resultOut, 5]];
bsf2 = BSplineFunction[Mean /@ GatherBy[resultOut, First]];
Row[
 ParametricPlot[#[x], {x, 0, 1}, ImageSize -> 200] & /@
  {bsf1, bsf2}]



Bob Hanlon




On Thu, Apr 25, 2013 at 2:52 AM, Dave Waddell <dwwaddell at gmail.com> wrote:

> On 4/20/13 4:41 AM, Dave Waddell wrote:
> > I tried converting the result image to a graph so that I could apply a
> > moving average and then fit a B-spline through it. As you can tell I'm
> > new to Mathematica:
> > data = ArrayRules@SparseArray@ImageData[result]
> > It was all downhill after that. Another nudge would be appreciated.
> > Thanks, Dave.
> >
> > Dave,
> >
> > On 4/17/13 1:30 AM, Dave Waddell wrote:
> >> I have a magnified image of a 0.1mm line here:
> >> http://www.d-a-v-e.org/images/Trace.jpg
> >> ... this converts with Binarize very well:
> >> http://www.d-a-v-e.org/images/Trace%20binary.jpg
> >> ... but what I would like to do is convert it to a single pixel wide
> > smoothed line running right up the middle. Any suggestions or pointers
> > on how to do this in Mathematica would be appreciated.
> >> Dave
> >>
> >
> > The sequence below seems like a good start.
> > The documentation for the functions should help you understand what is
> > going on in more details:
> >
> > trace = Import["http://www.d-a-v-e.org/images/Trace.jpg";]
> >
> > b = ColorNegate@Binarize[trace];
> > b2 = SelectComponents[b, "Area", -1];
> > b3 = FillingTransform@b2;
> > dt = ImageAdjust@DistanceTransform@b3; result =
> > ColorNegate@Image[WatershedComponents[dt], "Bit"];
> > HighlightImage[trace, result]
> >
> >
> > Matthias Odisio
> > Wolfram Research
>
> ImageValuePositions will give you the coordinates of the white pixels:
>
> In[21]:= ImageValuePositions[Image[IdentityMatrix[3], "Bit"], 1]
>
> Out[21]= {{0.5, 2.5}, {1.5, 1.5}, {2.5, 0.5}}
>
> Please note that ImageValuePositions does not sort the returned positions
> in
> any specific order.
>
> Matthias
>
> So I think I'm really close:
> resultOut =  ImageValuePositions[Image[WatershedComponents[dt], "Bit"], 0]
> BSplineFunction[MovingAverage[resultOut, 5]]
> ParametricPlot[%170[x], {x, -8, 8}]
>
> ... but I feel I could do much better and make it smoother. All suggestions
> are much appreciated.
> Dave
>
>
>

• References:
  • Converting a magnified image of a line to a single pixel smoothed
    • From: Dave Waddell <dwwaddell@gmail.com>