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b(With)12 b(the)h(naming)75 2628 y(sc)o(heme)h(from)e(Section)i(3,)f(the)i (original)d(outlines)h(are)h(similar,)d(but)j(with)g(con)o(trol)f(p)q(oin)o (ts)h(of)f(the)h(form)f(\()p Fl(\030)1785 2634 y Fh(j)1802 2628 y Fl(;)7 b(\021)1842 2634 y Fh(j)1859 2628 y Fx(\))p eop %%Page: 37 6 bop 927 -145 a Fx(-)13 b(37)h(-)244 2078 y @beginspecial @setspecial %%BeginDocument: procs.ps 13 13 scale 1 setlinecap 1 setlinejoin .04 setlinewidth 11 dict begin /ahu .35 def /aa { /y1 exch def /x1 exch def y1 sub /dy exch def x1 sub /dx exch def /ctm 6 array currentmatrix def x1 y1 translate dy dx atan rotate /r dx dx mul dy dy mul add sqrt def .8 ahu mul .5 ahu mul moveto 0 0 lineto .8 ahu mul -.5 ahu mul lineto 0 0 moveto r 0 lineto stroke ctm setmatrix} def /bdx 8 def /bx {/h exch def moveto bdx 0 rlineto 0 h rlineto bdx neg 0 rlineto closepath} def 8 28 moveto 14 29 1 -90 90 arc 8 29 1 90 270 arc 0 25 2 bx 14 23 4 bx 0 17 4 bx 11 19 2 bx 0 10 4 bx 11 8 3 bx 0 2 4 bx /bdx 6 def 16 13 4 bx 11 2 4 bx 22 8 moveto 27 8 27 11 1 arcto 4 {pop} repeat 27 11 21 11 1 arcto 4 {pop} repeat 21 11 21 8 1 arcto 4 {pop} repeat 21 8 27 8 1 arcto 4 {pop} repeat 20 1 moveto 25 1 25 4 1 arcto 4 {pop} repeat 25 4 19 4 1 arcto 4 {pop} repeat 19 4 19 1 1 arcto 4 {pop} repeat 19 1 25 1 1 arcto 4 {pop} repeat stroke 7.293 28.293 6 27 aa 14.707 28.293 16 27 aa 8 26 14 26 aa 4 25 4 21 aa 6 21 moveto 6 23.5 lineto stroke 6 23.5 14 23.5 aa 16 23 16 21 aa 19 20 moveto 1 0 rlineto stroke 20 20 20 17 aa 14 19 14 11 aa 6 14 moveto 6 16 lineto 13 16 lineto stroke 13 16 13 19 aa 4 17 4 14 aa 22 15 moveto 24 15 lineto stroke 24 15 24 11 aa 17 5.4 moveto 20 6 lineto stroke 20 6 20 13 aa 14 8 14 6 aa 6 6 moveto 6 9 lineto stroke 6 9 11 9 aa 4 10 4 6 aa 17 3 19 3 aa end %%EndDocument @endspecial 688 517 a(Original)f(outlines)263 680 y(Find)g(medial)f(axes)j Fj(x)p Fx(3.2)1028 684 y(Find)f(single-c)o(haracter)1028 734 y(distortion)f(measures)1028 784 y Fj(x)p Fx(3.1,)g(3.5,)f(3.6,)h(3.7)273 984 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61 y Fx(It)h(is)g(relativ)o(ely)f (simple)f(to)i(a)o(v)o(oid)f(misalignm)n(en)o(t)f(problems)h(suc)o(h)h(as)h (that)f(sho)o(wn)f(in)h(Figure)g(12)f(when)75 111 y(using)k(outlines)f(that)h (are)h(adjusted)f(to)g(the)g(pixel)g(grid.)29 b(All)18 b(that)f(is)h (required)h(is)f(to)g(use)g(the)h(information)75 160 y(deriv)o(ed)c(in)e (Section)i(3.3)e(for)g(determining)g(whic)o(h)h(p)q(oin)o(ts)g(on)g(the)g(c)o (haracter)i(outline)d(are)i(critical)e(for)h(v)o(ertical)75 210 y(and)h(horizon)o(tal)g(p)q(osition.)21 b(In)15 b(the)h(example)e(of)h (Figure)g(12,)g(b)q(oth)h Fl(A)f Fx(and)g Fl(B)j Fx(ma)o(y)13 b(b)q(e)j(recognized)h(as)e(ha)o(ving)75 260 y(imp)q(ortan)o(t)j Fl(x)h Fx(co)q(ordinates)i(since)f(they)h(are)f(b)q(oth)g(in)o(teger)g (adjustmen)o(t)f(p)q(oin)o(ts)g(with)h(in)o(teger-constrained)75 310 y Fl(x)14 b Fx(co)q(ordinates.)179 383 y(Although)d(it)h(is)g(p)q (ossible)h(to)f(use)h(virtually)e(an)o(y)h(criteria)g(to)g(decide)h(whic)o(h) f(pairs)h(of)e(in)o(teger)i(adjustmen)o(t)75 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y Fl(\030)1161 675 y Fh(n)1193 669 y Fj(\000)j Fl(X)1269 675 y Fh(n)1292 669 y Fx(\))493 b(\(18\))75 757 y(for)11 b(eac)o(h)g(pair)g(of)f(in)o(teger)h (adjustmen)o(t)f(p)q(oin)o(ts)h(\()p Fl(\030)857 763 y Fh(m)889 757 y Fl(;)c(\021)929 763 y Fh(m)960 757 y Fx(\))k(and)g(\()p Fl(\030)1099 763 y Fh(n)1122 757 y Fl(;)c(\021)1162 763 y Fh(n)1183 757 y Fx(\))k(where)h Fl(x)f Fx(co)q(ordinates)h(are)f(giv)o(en)g(in)o(teger) 75 806 y(constrain)o(ts.)19 b(Similarly)10 b(a)k(distortion)f(measure)648 856 y Fg(p)p 689 856 225 2 v 689 894 a Fl( )716 900 y Fs(2)735 894 y Fx(\()p Fl(\021)772 900 y Fh(m)812 894 y Fj(\000)d Fl(\021)875 900 y Fh(n)897 894 y Fx(\))d(\()p Fl(Y)960 900 y Fh(m)1001 894 y Fj(\000)13 b Fx(\026)-24 b Fl(\021)1064 900 y Fh(m)1104 894 y Fx(+)13 b(\026)-24 b Fl(\021)1167 900 y Fh(n)1198 894 y Fj(\000)9 b Fl(Y)1263 900 y Fh(n)1286 894 y Fx(\))499 b(\(19\))75 981 y(is)14 b(used)h(when)g Fl(y)h Fx(co)q(ordinates)f(are)f(giv)o(en)g(in)o (teger)h(constrain)o(ts.)20 b(Note)14 b(that)g(\()1333 970 y(\026)1329 981 y Fl(\030)1347 987 y Fh(m)1379 981 y Fl(;)c Fx(\026)-24 b Fl(\021)1419 987 y Fh(m)1450 981 y Fx(\))14 b(and)g(\()p Fl(X)1611 987 y Fh(m)1643 981 y Fl(;)7 b(Y)1686 987 y Fh(m)1717 981 y Fx(\))15 b(are)f(the)75 1031 y(scaled)g(and)g(adjusted)h(v)o(ersions)f (of)f(\()p Fl(\030)684 1037 y Fh(m)716 1031 y Fl(;)7 b(\021)756 1037 y Fh(m)787 1031 y Fx(\))14 b(and)f Fl( )924 1037 y Fs(2)957 1031 y Fx(is)h(a)f(w)o(eigh)o(ting)g(function)h(something)e(lik)o(e)667 1143 y Fl( )694 1149 y Fs(2)713 1143 y Fx(\()p Fl(x)p Fx(\))g(=)829 1115 y(100)p 829 1133 63 2 v 832 1171 a Fl(H)870 1159 y Fs(2)904 1143 y Fx(exp)974 1084 y Fg(\022)1005 1143 y Fj(\000)1044 1097 y Fg(\020)1117 1115 y Fl(x)p 1073 1133 112 2 v 1073 1171 a Fx(0)p Fl(:)p Fx(03)p Fl(H)1190 1097 y Fg(\021)1215 1105 y Fs(2)1234 1084 y Fg(\023)1271 1143 y Fl(:)75 1278 y Fv(4.)48 b(The)15 b(F)l(on)o(t-Wide)f(Distortio)o(n)f(F)l(unction)179 1360 y Fx(Since)g(some)f(features)i(suc)o(h)f(as)g(baseline,)g(x-heigh)o(t,)f (and)g(the)i(width)e(of)g(main)f(v)o(ertical)h(stems)h(should)f(b)q(e)75 1410 y(uniform)f(across)i(the)h(fon)o(t)e(as)h(a)f(whole,)h(it)f(is)h (desirable)g(to)g(ha)o(v)o(e)f(a)h(separate)h(distortion)e(function)h(to)f (allo)o(w)f(the)75 1459 y(parameters)j(to)g(b)q(e)g(c)o(hosen)h(once)g(and)e (used)i(for)f(ev)o(ery)g(c)o(haracter)i(in)d(the)h(fon)o(t.)179 1533 y(An)k(imp)q(ortan)o(t)e(prop)q(ert)o(y)j(of)e(the)h(parameters)g(that)g (need)h(fon)o(t-wide)e(con)o(trol)h(is)f(that)h(they)h(all)d(ha)o(v)o(e)75 1582 y(in)o(teger)c(v)n(alues.)17 b(F)m(or)10 b(instance,)j(the)e(baseline,)h (the)g(x-heigh)o(t,)f(and)g(all)f(the)i(other)g(heigh)o(ts)f(mark)o(ed)f(in)h (Figure)g(13)75 1632 y(o)q(ccur)i(at)f(in)o(teger)g(adjustmen)o(t)g(p)q(oin)o (ts)f(that)i(are)f(to)g(b)q(e)h(giv)o(en)e(in)o(teger)i Fl(y)q Fx(-v)n(alues.)k(Additionally)m(,)10 b(in)o(teger)i(v)n(alues)75 1682 y(are)i(also)g(needed)h(to)f(describ)q(e)h(width)f(features)h(suc)o(h)g (as)f(the)g(width)g(of)f(v)o(ertical)h(stems.)179 1755 y(This)g(suggests)i (that)f(the)h(fon)o(t-wide)e(parameters)g(can)h(b)q(e)h(describ)q(ed)g(b)o(y) f(in)o(teger-v)n(alued)f(v)n(ariables)g Fl(P)1845 1761 y Fs(1)1863 1755 y Fx(,)75 1805 y Fl(P)102 1811 y Fs(2)120 1805 y Fx(,)g(.)7 b(.)g(.)n(,)13 b(that)h(can)g(b)q(e)h(c)o(hosen)g(b)o(y)e(minimi)o(zing)e(a)j (distortion)f(function)h(of)f(the)h(form)792 1892 y Fl(T)822 1875 y Fs(2)816 1902 y(1)850 1892 y Fx(+)c Fl(T)922 1875 y Fs(2)916 1902 y(2)950 1892 y Fx(+)f Fl(T)1021 1875 y Fs(2)1015 1902 y(3)1049 1892 y Fx(+)h Fj(\001)d(\001)g(\001)e Fl(;)75 1979 y Fx(where)14 b(eac)o(h)f Fl(T)310 1985 y Fh(i)337 1979 y Fx(is)g(is)g(a)f(linear)g(expression)i(in)o(v)o(olving)d Fl(P)969 1985 y Fs(1)987 1979 y Fx(,)i Fl(P)1039 1985 y Fs(2)1057 1979 y Fx(,)f Fl(P)1108 1985 y Fs(3)1127 1979 y Fx(,)g(.)7 b(.)g(.)f(.)17 b(F)m(or)c(instance,)g(if)f Fl(P)1546 1985 y Fs(1)1577 1979 y Fx(is)h(the)g(cap)g(heigh)o(t)75 2029 y(and)e Fl(P)180 2035 y Fs(2)210 2029 y Fx(is)g(the)h(ascender)h(heigh)o(t,)e(there)i (migh)o(t)c(b)q(e)j(a)g(fon)o(t-wide)e(distortion)h(measure)g Fl(T)1475 2035 y Fs(17)1522 2029 y Fx(=)h Fl(P)1593 2035 y Fs(1)1616 2029 y Fj(\000)t Fl(P)1679 2035 y Fs(2)1702 2029 y Fx(+)6 b(\026)-23 b Fl(\031)1762 2035 y Fs(2)1785 2029 y Fj(\000)6 b Fx(\026)-23 b Fl(\031)1845 2035 y Fs(1)1863 2029 y Fx(,)75 2079 y(where)14 b(\026)-23 b Fl(\031)216 2085 y Fs(1)245 2079 y Fx(and)13 b(\026)-23 b Fl(\031)347 2085 y Fs(2)376 2079 y Fx(represen)o(t)13 b(the)e(desired)h(v)n(alues)f(of)f Fl(P)950 2085 y Fs(1)979 2079 y Fx(and)h Fl(P)1084 2085 y Fs(2)1113 2079 y Fx(giv)o(en)f(as)h(a\016ne)g(functions)f(of)h(the)g(scale)g(factor.) 179 2152 y(Since)f(the)h Fl(P)6 b Fu(-variables)13 b Fl(P)597 2158 y Fs(1)615 2152 y Fx(,)d Fl(P)664 2158 y Fs(2)683 2152 y Fx(,)g(.)d(.)g(.)h(represen)o(t)13 b(features)e(that)f(are)h(con)o(trolled) f(b)o(y)g(the)h Fl(I)s Fx(-v)n(ariables)f(for)f(the)75 2202 y(c)o(haracters)16 b(in)o(v)o(olv)o(ed,)c(it)i(mak)o(es)f(sense)i(to)f(in)o (tro)q(duce)h(the)g Fl(P)6 b Fx(-v)n(ariables)12 b(in)o(to)i(the)g(single-c)o (haracter)h(distortion)75 2252 y(function)g(b)o(y)g(substituting)g(com)o (binations)e(of)h Fl(P)6 b Fx(-v)n(ariables)14 b(for)h Fl(I)s Fx(-v)n(ariables.)21 b(In)15 b(the)h(case)g(of)e(Figure)i(30,)e(this)75 2302 y(could)g(b)q(e)g(done)g(b)o(y)g(writing)f(do)o(wn)h(the)g(relations)515 2389 y Fl(I)533 2395 y Fs(10)578 2389 y Fj(\000)c Fl(I)638 2395 y Fs(7)668 2389 y Fx(=)i Fl(P)739 2395 y Fs(3)769 2389 y Fx(=)f(width)j(of)f(curv)o(ed)i(horizon)o(tal)e(strok)o(es)532 2451 y Fl(I)550 2457 y Fs(4)578 2451 y Fj(\000)d Fl(I)638 2457 y Fs(2)668 2451 y Fx(=)i Fl(P)739 2457 y Fs(4)769 2451 y Fx(=)f(width)j(of)f (straigh)o(t)h(horizon)o(tal)f(strok)o(es)499 2513 y Fl(I)517 2519 y Fs(12)562 2513 y Fj(\000)c Fl(I)621 2519 y Fs(14)668 2513 y Fx(=)j Fl(P)739 2519 y Fs(4)769 2513 y Fx(=)f(width)j(of)f(straigh)o (t)h(horizon)o(tal)f(strok)o(es)603 2576 y Fl(I)621 2582 y Fs(10)668 2576 y Fx(=)f Fl(P)739 2582 y Fs(1)769 2576 y Fx(=)f(cap)k(heigh)o (t)620 2638 y Fl(I)638 2644 y Fs(1)668 2638 y Fx(=)d Fl(P)739 2644 y Fs(5)769 2638 y Fx(=)f(baseline)j(heigh)o(t)720 b(\(20\))p eop %%Page: 22 21 bop 927 -145 a Fx(-)13 b(22)h(-)75 -21 y(at)i(\()p Fl(X)178 -15 y Fh(a)p Fs(2)215 -21 y Fl(;)7 b(Y)258 -15 y Fh(a)p Fs(2)294 -21 y Fx(\))17 b(and)e(\()p Fl(X)459 -15 y Fh(b)p Fs(2)493 -21 y Fl(;)7 b(Y)536 -15 y Fh(b)p Fs(2)569 -21 y Fx(\).)25 b(Using)16 b Fl(d)763 -15 y Fh(ab)812 -21 y Fx(=)865 -37 y Fs(1)p 865 -30 17 2 v 865 -6 a(2)893 -21 y Fj(k)p Fl(D)q Fj(k)p Fx(,)g(the)h(argumen)o(t)e(used)i(to)f(deriv)o(e)h(\(1\))f(sho)o(ws)g(that)g (the)75 29 y(distortion)d(measures)558 103 y(\(\001)609 109 y Fh(a)638 103 y Fx(+)d(\001)715 109 y Fh(b)731 103 y Fx(\))747 37 y Fg(r)p 789 37 112 2 v 794 75 a Fl(\013)821 81 y Fs(6)839 75 y Fl(d)861 81 y Fh(ab)p 794 93 102 2 v 834 131 a Fx(4)942 103 y(and)41 b(\(\001)1101 109 y Fh(b)1127 103 y Fj(\000)9 b Fx(\001)1203 109 y Fh(a)1223 103 y Fx(\))1239 37 y Fg(r)p 1280 37 112 2 v 1285 75 a Fl(\013)1312 81 y Fs(6)1331 75 y Fl(d)1353 81 y Fh(ab)p 1285 93 102 2 v 1315 131 a Fx(12)1801 103 y(\(16\))75 197 y(con)o(tribute)k(to)f(the)g(total)g(distortion)f(a)h(w)o (eigh)o(ting)f(factor)h Fl(\013)1038 203 y Fs(6)1068 197 y Fj(\031)g Fx(5)6 b Fj(\002)g Fx(10)1219 182 y Fs(5)1236 197 y Fl(=H)1295 182 y Fs(3)1326 197 y Fx(times)11 b(the)i(in)o(tegral)e(with)h (resp)q(ect)75 247 y(to)i(arc)g(length)g(of)f(the)i(squared)f(p)q(erp)q (endicular)h(displacemen)o(t.)75 363 y Fv(3.6.)48 b(Width)14 b(Matc)o(hing)179 447 y Fx(Figures)g(2)g(and)g(14)f(clearly)h(demonstrated)g (the)g(need)h(for)f(con)o(trolling)f(relativ)o(e)g(strok)o(e)i(widths)f(in)g (scan-)75 496 y(con)o(v)o(erted)i(bitmaps.)21 b(As)15 b(suggested)i (previously)m(,)d(this)i(con)o(trol)e(can)i(b)q(e)g(ac)o(hiev)o(ed)f(b)o(y)g (making)e(sure)j(that)f(the)75 546 y(outlines)f(are)g(adjusted)h(to)f(\014t)g 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