Between the Lines

Octave, 233 225 216 213 bytes

o=@ones;l=z=o(5,1);for k=input('')-47;l=[l,reshape(dec2bin([448,22558,8514,10560,3936,2376,328,15840,320,2368](k),15),5,[])-48,z];end;L=~o(size(l)+2);L(2:6,2:end-1)=l;O=o(3);O(5)=-8;M=~conv2(kron(L,o(25)),O);imshow(M)

Here the first test case (from a resized screen capture, s.t. it fits my monitor=):

o=@ones;
l=z=o(5,1);                   %spacer matrices
for k=input('')-47;           %go throu all input digis
                              %decode the matrices for each digit from decimal
l=[l,reshape(dec2bin([448,22558,8514,10560,3936,2376,328,15840,320,2368](k),15),5,[])-48,z];
end
L=~o(size(l)+2);           %pad the image
L(2:6,2:end-1)=l;
O=o(3);O(5)=-8;               %create edge detection filter
imshow(~conv2(kron(L,o(25)),O)) %image resizing /edge detection (change 25 to any cell size you like)

The input can be arbitrary length, like e.g. '07299361548'

Convolution is the key to success.

Html+JavaScript ES6, 352

Test running the snippet below

<canvas id=C></canvas><script>s=prompt(),C.width=-~s.length*80,c=C.getContext("2d"),[...s].map(d=>[30,d*=3,++d,++d].map(w=a=>{for(a=parseInt("vhvivgtlnllv74vnltvlt11vvlvnlv0"[a],36)*2+1,p=1,y=100,i=64;i>>=1;p=b,y-=20)c.moveTo(x+20,y),b=a&i?1:0,c[b-p?'lineTo':'moveTo'](x,y),(a^q)&i&&c.lineTo(x,y-20);q=a,x+=20}),q=63,x=0),w(30),w(0),c.stroke()</script>

Less golfed

s=prompt(),C.width=-~s.length*80,c=C.getContext("2d"),
w=a=>{
  a=parseInt("vhvivgtlnllv74vnltvlt11vvlvnlv0"[i],36)*2+1
  for(p=1,y=100,i=32;i;p=b,y-=20,i>>=1)
    c.moveTo(x+20,y),
    b=a&i?1:0,
    c[b-p?'lineTo':'moveTo'](x,y),
    (a^q)&i&&c.lineTo(x,y-20)
  q=a 
  x+=20
},
[...s].map(d=>[30,d*=3,++d,++d].map(w),q=63,x=0),
w(30),w(0)
c.stroke()

Javascript ES6, 506 bytes

a=>{with(document)with(body.appendChild(createElement`canvas`))with(getContext`2d`){width=height=(a.length+2)*80;scale(20,20);translate(1,1);lineWidth=0.1;beginPath();["oint",...a.map(i=>"05|7agd7|oint 067128a45|oicgmnt 01de25|oil9amnt 01de23fg45|oint 03fh5|68ec6|oint 03fg45|oij78knt 05|9agf9|oij78knt 01dh5|oint 05|78ed7|9agf9|oint 03fg45|78ed7|oint".split` `[i]),"05"].map(i=>{i.split`|`.map(i=>[...i].map((e,i,_,p=parseInt(e,36),l=~~(p/6),r=p%6)=>i?lineTo(l,r):moveTo(l,r)));translate(4,0)});stroke()}}

Ungolfed:

a=>{                                            // anonymous function declaration, accepts array of numbers
  with(document)                                // bring document into scope
  with(body.appendChild(createElement`canvas`)) // create canvas, drop into html body, bring into scope
  with(getContext`2d`){                         // bring graphics context into scope
    width=height=(a.length+2)*80;               // set width and height
    scale(20,20);                               // scale everything to 20x
    translate(1,1);                             // add padding so outline doesn't touch edge of canvas
    lineWidth=0.1;                              // have to scale line width since we scaled 20x
    beginPath();                                // start drawing lines
    ["oint",                                    // beginning "glyph", draws left end of negative space, see below
     ...a.map(i=>`05|7agd7|oint                 // glyphs 0-9 encoded as vertices
                  067128a45|oicgmnt             //   glyphs seperated by " "
                  01de25|oil9amnt               //   lines within each glyph seperated by "|"
                  01de23fg45|oint               //   a single vertex is stored as a base36 char
                  03fh5|68ec6|oint              //     where a number corresponds to one of the verts shown below:
                  03fg45|oij78knt               //        0  6 12 18 24
                  05|9agf9|oij78knt             //        1  7 13 19 25
                  01dh5|oint                    //        2  8 14 20 26
                  05|78ed7|9agf9|oint           //        3  9 15 21 27
                  03fg45|78ed7|oint`            //        4 10 16 22 28
       .split` `[i]),                           //        5 11 17 23 29
     "05"]                                      // end "glyph", draws right end of negative space, see above
      .map(i=>{                                 // for each glyph string
        i.split`|`                              // seperate into list of line strings
          .map(i=>[...i]                        // convert each line string into list of chars
            .map((e,i,_,p=parseInt(e,36),       // convert base36 char to number
                  l=~~(p/6),r=p%6)=>            // compute x y coords of vertex
              i?lineTo(l,r):moveTo(l,r)));      // draw segment
        translate(4,0)});                       // translate origin 4 units to right
    stroke()}}                                  // draw all lines to canvas

Assumes there's a <body> to append the canvas to, tested in Firefox 46.

Example run (assigning anonymous function to f):

f([1,0,3])

yields: