Screening of an element for to get displacement, speed and acceleration

Question

I am launching a study to capture the path made by a circle with a cross that indicates the zero point of the system.

I searched some reference and a good proposal was this:

Visualization of tracks of objects in images by superposition

I don't have a lot of practice with the software, but I believe that to trace the circle command is ImageMeasurements.

I want to go a little further, I intend to obtain the relative coordinates of the circle with the center of the cross.

With this I could calculate the displacements, velocities and accelerations.

I just posted the matter for soon I will be able to enter a initial code.

Below is a link to a file MP4:

File MP4

Answer 1

Solution using PixelValuePositions

---

getting the coordinates of the element in 1 image.

edgeCoordinates = 
   PixelValuePositions[
               EdgeDetect[
                       First[
                         Import["https://i.imgur.com/irikm2L.gif", "GIF"]]],1]

>

Graphics[Point[edgeCoordinates]]

>

remove the frame

withoutFrame = 
  edgeCoordinates //. {a_, b_} /; (a == 2 \[Or] b == 500 \[Or] b ==499 \[Or] b == 2 \[Or] a == 500 \[Or] b == 1) :> Nothing

Graphics[Point[withoutFrame], PlotRange -> {{1, 500}, {1, 500}}]

I think you should get the relative coordinates of the circle with respect to the bottom left corner {0,0}.

removing the cross

So now I will remove the cross and give you the coordinates of the ball in all images...

Graphics[Point[withoutCross = withoutFrame /. 
Evaluate[# -> Nothing & /@ {{249, 67}, {250, 67}, {251, 67}, {252,
     67}, {249, 66}, {252, 66}, {249, 65}, {252, 65}, {249, 
    64}, {252, 64}, {249, 63}, {252, 63}, {249, 62}, {252, 
    62}, {249, 61}, {252, 61}, {249, 60}, {252, 60}, {249, 
    59}, {252, 59}, {249, 58}, {252, 58}, {249, 57}, {252, 
    57}, {249, 56}, {252, 56}, {249, 55}, {252, 55}, {249, 
    54}, {252, 54}, {249, 53}, {252, 53}, {234, 52}, {235, 
    52}, {236, 52}, {237, 52}, {238, 52}, {239, 52}, {240, 
    52}, {241, 52}, {242, 52}, {243, 52}, {244, 52}, {245, 
    52}, {246, 52}, {247, 52}, {248, 52}, {249, 52}, {252, 
    52}, {253, 52}, {254, 52}, {255, 52}, {256, 52}, {257, 
    52}, {258, 52}, {259, 52}, {260, 52}, {261, 52}, {262, 
    52}, {263, 52}, {264, 52}, {265, 52}, {266, 52}, {267, 
    52}, {234, 51}, {267, 51}, {234, 50}, {267, 50}, {235, 
    49}, {236, 49}, {237, 49}, {238, 49}, {239, 49}, {240, 
    49}, {241, 49}, {242, 49}, {243, 49}, {244, 49}, {245, 
    49}, {246, 49}, {247, 49}, {248, 49}, {249, 49}, {252, 
    49}, {253, 49}, {254, 49}, {255, 49}, {256, 49}, {257, 
    49}, {258, 49}, {259, 49}, {260, 49}, {261, 49}, {262, 
    49}, {263, 49}, {264, 49}, {265, 49}, {266, 49}, {249, 
    48}, {252, 48}, {249, 47}, {252, 47}, {249, 46}, {252, 
    46}, {249, 45}, {252, 45}, {249, 44}, {252, 44}, {249, 
    43}, {252, 43}, {249, 42}, {252, 42}, {249, 41}, {252, 
    41}, {249, 40}, {252, 40}, {249, 39}, {252, 39}, {249, 
    38}, {252, 38}, {249, 37}, {252, 37}, {249, 36}, {252, 
    36}, {249, 35}, {252, 35}, {250, 34}, {251, 34}}]], 
    PlotRange -> {{1, 500}, {1, 500}}]

a general function...

cleanImage[image_] := (((PixelValuePositions[EdgeDetect[image], 1])//. {a_, b_} /; (a == 2 \[Or] b == 500 \[Or] b == 499 \[Or] 
     b == 2 \[Or] a == 500 \[Or] b == 1) :> Nothing) /. Evaluate[# -> Nothing & /@ {{249, 67}, {250, 67}, {251, 67}, {252, 
   67}, {249, 66}, {252, 66}, {249, 65}, {252, 65}, {249, 
   64}, {252, 64}, {249, 63}, {252, 63}, {249, 62}, {252, 
   62}, {249, 61}, {252, 61}, {249, 60}, {252, 60}, {249, 
   59}, {252, 59}, {249, 58}, {252, 58}, {249, 57}, {252, 
   57}, {249, 56}, {252, 56}, {249, 55}, {252, 55}, {249, 
   54}, {252, 54}, {249, 53}, {252, 53}, {234, 52}, {235, 
   52}, {236, 52}, {237, 52}, {238, 52}, {239, 52}, {240, 
   52}, {241, 52}, {242, 52}, {243, 52}, {244, 52}, {245, 
   52}, {246, 52}, {247, 52}, {248, 52}, {249, 52}, {252, 
   52}, {253, 52}, {254, 52}, {255, 52}, {256, 52}, {257, 
   52}, {258, 52}, {259, 52}, {260, 52}, {261, 52}, {262, 
   52}, {263, 52}, {264, 52}, {265, 52}, {266, 52}, {267, 
   52}, {234, 51}, {267, 51}, {234, 50}, {267, 50}, {235, 
   49}, {236, 49}, {237, 49}, {238, 49}, {239, 49}, {240, 
   49}, {241, 49}, {242, 49}, {243, 49}, {244, 49}, {245, 
   49}, {246, 49}, {247, 49}, {248, 49}, {249, 49}, {252, 
   49}, {253, 49}, {254, 49}, {255, 49}, {256, 49}, {257, 
   49}, {258, 49}, {259, 49}, {260, 49}, {261, 49}, {262, 
   49}, {263, 49}, {264, 49}, {265, 49}, {266, 49}, {249, 
   48}, {252, 48}, {249, 47}, {252, 47}, {249, 46}, {252, 
   46}, {249, 45}, {252, 45}, {249, 44}, {252, 44}, {249, 
   43}, {252, 43}, {249, 42}, {252, 42}, {249, 41}, {252, 
   41}, {249, 40}, {252, 40}, {249, 39}, {252, 39}, {249, 
   38}, {252, 38}, {249, 37}, {252, 37}, {249, 36}, {252, 
   36}, {249, 35}, {252, 35}, {250, 34}, {251, 34}}])

 images30 = Take[Import["https://i.imgur.com/irikm2L.gif", "GIF"], 500];

 images166 = images30[[Range[1, 501, 3]]];

 ListAnimate[(Graphics[{PointSize[.02],    
      Point[Mean[(cleanImage[#])]]}, 
        PlotRange -> {{0, 500}, {0, 500}}] & /@ images166)]

Show[(Graphics[{PointSize[.02], Point[Mean[(cleanImage[#])]]}, 
 PlotRange -> {{0, 500}, {0, 500}}] & /@ 
   Import["https://i.imgur.com/irikm2L.gif", "GIF"][[Range[1, 501, 3]]])]

---

vector function of displacement through time

images166 = Take[Import["https://i.imgur.com/irikm2L.gif", "GIF"], 500][[Range[1, 501, 3]]];
pts = Mean[(cleanImage[#])] & /@images166;
X[t_] := ListInterpolation[Transpose[pts][[1]]][t]
Y[t_] := ListInterpolation[Transpose[pts][[2]]][t]

speed

D[ X[t], t]
D[ Y[t], t]

acceleration

D[D[X[t], t],t]
D[D[X[t], t],t]