Here we have 3 sets of coordinates. Each set is just made up of 4 points forming 3 line segments.
In[]:=
images={​​{{0,190.88099670410156`},{2,230.89999389648438`},{7,201.6280059814453`},{12,248.83999633789062`}},{{0,146.5`},{18,224.63999938964844`},{23,118.5`},{75,248.38999938964844`}},{{0,176.52099609375`},{4,217.3000030517578`},{19,158.83999633789062`},{44,248.38999938964844`}}​​};​​
Then we plot the images and we get
In[]:=
​​(*Weplotthe3imagesandwegettheimagesbelow*)​​plots=Table[ListLinePlot[images[[n]],Background->Black,ImageSize{128,128},Frame->True,Axes->False,AspectRatio1,PlotMarkers{{●,2}}],{n,1,Length[images]}]​​
Out[]=

,
,

Let us now Binarize the images
In[]:=
​​Binarize[#]&/@plots​​
Out[]=

,
,

So far so good. However, I want the plots to only have a single black frame around them. So, based on suggestions from Rohit and Henrik I do this:
In[]:=
plots=Table[ListLinePlot[images[[n]],Background->Black,ImageSize{128,128},Frame->False,Axes->False,AspectRatio1,PlotMarkers{{●,2}}]//Framed,{n,1,Length[images]}]​​
Out[]=

,
,

Above is what I want (except for the 2nd image which somehow does not fill the whole Y range like the 2 outside plots). Also, now, I can no longer binarize the image
In[]:=
Binarize[#]&/@plots(*Thatlastcommandgivesanerror*)​​
Binarize
:Expecting an image or graphics instead of
.
Binarize
:Expecting an image or graphics instead of
.
Binarize
:Expecting an image or graphics instead of
.
General
:Further output of Binarize::imginv will be suppressed during this calculation.
Out[]=
Binarize
,Binarize
,Binarize

But if I remove the frame. as in
​
In[]:=
plots=Table[ListLinePlot[images[[n]],Background->Black,ImageSize{128,128},Frame->False,Axes->False,AspectRatio1,PlotMarkers{{●,2}}],{n,1,Length[images]}]​​
Out[]=

,
,

I can, again, binarize the images
In[]:=
Binarize[#]&/@plots​​
Out[]=

,
,

​