id sid tid token lemma pos np193774991 1 1 any any DET np193774991 1 2 subset subset NOUN np193774991 1 3 of of ADP np193774991 1 4 the the DET np193774991 1 5 plane plane NOUN np193774991 1 6 can can AUX np193774991 1 7 be be AUX np193774991 1 8 approximated approximate VERB np193774991 1 9 by by ADP np193774991 1 10 a a DET np193774991 1 11 set set NOUN np193774991 1 12 of of ADP np193774991 1 13 square square ADJ np193774991 1 14 pixels pixel NOUN np193774991 1 15 . . PUNCT np193774991 2 1 unfortunately unfortunately ADV np193774991 2 2 , , PUNCT np193774991 2 3 while while SCONJ np193774991 2 4 this this DET np193774991 2 5 pixelation pixelation NOUN np193774991 2 6 looks look VERB np193774991 2 7 similar similar ADJ np193774991 2 8 to to ADP np193774991 2 9 the the DET np193774991 2 10 original original ADJ np193774991 2 11 set set NOUN np193774991 2 12 , , PUNCT np193774991 2 13 it it PRON np193774991 2 14 does do AUX np193774991 2 15 not not PART np193774991 2 16 resemble resemble VERB np193774991 2 17 the the DET np193774991 2 18 original original ADJ np193774991 2 19 set set NOUN np193774991 2 20 closely closely ADV np193774991 2 21 from from ADP np193774991 2 22 a a DET np193774991 2 23 mathematical mathematical ADJ np193774991 2 24 perspective perspective NOUN np193774991 2 25 . . PUNCT np193774991 3 1 using use VERB np193774991 3 2 a a DET np193774991 3 3 technique technique NOUN np193774991 3 4 inspired inspire VERB np193774991 3 5 by by ADP np193774991 3 6 morse morse NOUN np193774991 3 7 theory theory NOUN np193774991 3 8 , , PUNCT np193774991 3 9 we we PRON np193774991 3 10 algorithmically algorithmically ADV np193774991 3 11 produce produce VERB np193774991 3 12 a a DET np193774991 3 13 pl pl PROPN np193774991 3 14 approximation approximation NOUN np193774991 3 15 of of ADP np193774991 3 16 the the DET np193774991 3 17 original original ADJ np193774991 3 18 shape shape NOUN np193774991 3 19 using use VERB np193774991 3 20 only only ADJ np193774991 3 21 information information NOUN np193774991 3 22 from from ADP np193774991 3 23 its its PRON np193774991 3 24 pixelation pixelation NOUN np193774991 3 25 . . PUNCT np193774991 4 1 this this DET np193774991 4 2 approximation approximation NOUN np193774991 4 3 converges converge VERB np193774991 4 4 to to ADP np193774991 4 5 the the DET np193774991 4 6 original original ADJ np193774991 4 7 shape shape NOUN np193774991 4 8 in in ADP np193774991 4 9 a a DET np193774991 4 10 very very ADV np193774991 4 11 strong strong ADJ np193774991 4 12 sense sense NOUN np193774991 4 13 : : PUNCT np193774991 4 14 as as SCONJ np193774991 4 15 the the DET np193774991 4 16 size size NOUN np193774991 4 17 of of ADP np193774991 4 18 the the DET np193774991 4 19 pixels pixel NOUN np193774991 4 20 goes go VERB np193774991 4 21 to to ADP np193774991 4 22 zero zero NUM np193774991 4 23 we we PRON np193774991 4 24 can can AUX np193774991 4 25 recover recover VERB np193774991 4 26 important important ADJ np193774991 4 27 geometric geometric ADJ np193774991 4 28 and and CCONJ np193774991 4 29 topological topological ADJ np193774991 4 30 invariants invariant NOUN np193774991 4 31 of of ADP np193774991 4 32 the the DET np193774991 4 33 original original ADJ np193774991 4 34 shape shape NOUN np193774991 4 35 such such ADJ np193774991 4 36 as as ADP np193774991 4 37 betti betti ADJ np193774991 4 38 numbers number NOUN np193774991 4 39 , , PUNCT np193774991 4 40 area area NOUN np193774991 4 41 , , PUNCT np193774991 4 42 perimeter perimeter NOUN np193774991 4 43 and and CCONJ np193774991 4 44 curvature curvature NOUN np193774991 4 45 measures measure NOUN np193774991 4 46 . . PUNCT