MIT Artificial Intelligence Laboratory Vision Grou

Griffith, Arnold K.

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Vision Flash 6March 1971How to Use .VSCANArnold K. GriffithVision GroupA.I. LaboratoryMJI.T.I. A COOKBOOK APPROACHThe call to .VSCAN looks like this:.VSCAN PTABLE,where the parameters governing the scan, pointedto by the tag PTABLE, are 11 in number:PTABLE: WBIT, ,VCONO-LENGTH,,ARRAYXRES,,YRESR1R2ClR3R4C2P1P2and the intensities end up stored in locationsARRAY ... ARRAY + XRES*YRES - 1.Scanning within some arbitrary quadrilateral onithe vidi field, e.g.;PT3PT4 .PT3. .. . . .A E*.... .......... .." ...... .. PT2PTIPT1Figure 1.is under control of these parameters, generated asfollows:Parameter 1 is described in the ITS manual;if in doubt, use 0,,3.Parameter 2 consists of the negative of thetotal number of points to be examined in the left half;and the starting address of the block into which theintensities are to be stored in the right haIf.Parameter 3 has the number of points in eachscan in the left half; and the number of scans in the righthalf.Parameters 4-11 are described in the ITS manual;however it is not obvious how one goes from the cornerpoints of a desired scan to the parameter values. Thefunction EIGHTVPARAM (in appendix) given the appropriateparameters, in order Ri, ... P2, given the corner pointsPT1, PT2, PT3 and PT4 (in the form (x y)). The relationbetween the resulting scanning pattern and the corner pointsis as shown in figure 1: If the point PT2 is directly abovePTI, then the scans will be made vertically; if the pointPT2 is to the right of PTI, the scans will be horizontal;if PT4 and PT3 are below PT1 and PT2, then each successivescan will be below the previous one; etc. The coordinatesystem of these pointe assumes that the vidi field goes from(0 0) to (1024. 1024. .II. HORIZONTAL AND VERTICAL SCANNING WITH SOME KNOWLEDGEOF WHAT IS GOING ONThe parameters R1, ... P2 are fixed point quantitieswith the binary point in the middle of the word. Thusif they have integer values, these integers should be storedin the left half. The origin of the scan is always (Cl,C2).Several simple cases:1) For a horizontal scan of length L, let R1=L andR2=R3=R4 P =P2=0.2) For a vertical scan of length L, let R3=L, andR1=R2 =R4--P l=P2 =0.3) For a vertically ascending sequence (of height H)of left-right horizontal scans of length L, (See figure 2)H " 41Ffigure 2.let RI=L R4=H and R2=R3=Pl=P2=0.4) For a sequence of ascending vertical scansof length L, with each successive scan to the right ofthe previous one (see figure 3) use 2W, 3=L and-;F- A A IL1Lfigure 3.Rl=R4=Pl=P2=0.In all cases, Cl and C2 are respectively thex and y coordinates of the starting point of the scan;and the number of points in each scan and the numberof scans determine the third parameter. The valuesCl, C2, L, W, and H are scaled conmmensurate with thevidi field being 400008 x 400008 units in extent.1`rk i ý d ý I k IcIII. WHAT IS REALLY GOING ONAccording to the ITS manual, .VSCAN generates aset of points (X2,Y2) within the unit square:(0,1) (1,1)0 0 0 0 0 0 0o o o o o o o oo o~0- o o o9-th 0 0(o,o0 (1,O0first 8-thfigure 4.which has been divided into XRESxYRES equal sub-rectangles;and each point is in the center of a sub-rectangle. Theorder Ln which the points is generated is as in figure 4,namely the XRES points of the bottom row of rectangelsis generated in left-right order, similarly the next-to-bottomrow, etc. The coordinates given to the vidissector consistof these points, in the order generated, transformed by thetransformation f(x,y):(X2,Y2) f(X2,Y2) = (X,Y):Rl*X2 + R2*Y2 + ClPl*X2 + P2*Y2 + 1R3*X2 + R4*Y2 + 02Y=Pl*X2 + P2*Y2 + 1Evidently the images of (0,0),(1,0),(l,l) and (0,1)under this transformation become the points PTI, PT2, PT3, andPT4 as in figure 1.5Letting:PT1 = (X1,Y1)PT2 = (X2,Y2)PT3 = (X3,Y3)PT4 = (X4,Y4)we have, from f(0,0) = (X1,Y1):x1 = Cl (1)Y1 = c2; (2)from f(1,0) = (X2,Y2):X2 = Pl + (3)R3 + C2 (4)Y2 P= +4)Pl + 1from f(l,l) = (X3,Y3):R1 + R2 + CIX3 = PI + P2 + (5)Y3 = R3 + R4 + C2Pl1+ P2 + 1and from f(0,1) = (X4,Y4):R2 + ClX4 = P2 + 1 (7)R4 + C2P2 + (8)letting:(a,a') = (X2-X1,Y2-Y1)(b,b') = (X4-X1,Y4-Y1)(c,c') = (X3-X2,Y3-Y2)(d,d') = (X3-X4,Y3-Y4),the equations (1), ...Cl = X1C2 = X2ad' - a'dcd' - c'dcb' - e'bcd' - c'dRI = X2P.1 + aR2 = X4P2 + bR3 = Y2PI + a'R4 = Y4P2 + b'.(8) solve to:Note: If the transformation f is in fact carried out asstated in the ITS manual, then any point (X2,Y2) s.t.PIX2 + P2Y2 + 1 = 0transforms into randomness, since this gives a zerodenomenator in the transformation formula. It isnot clear if this can really happen, but may accountfor lossage in some situations.APPENDIXPAGE 8: The function EIGHTVPARAMPAGE 9: Auxiliary functionsPAGE 10: A simple IAP function which uses theoutput of EIGHTVPARAM to drive the vidi.0i10O2 (DEFPROP EIGHTVPARAM(LAMBDA(PT1 PT2 PTI OT4)00U3 (PHUG(A B C D Pi P2 Cl C2 R13 R24)OU4 (StTU PTI(SCALE P11))OU05 (SLTU PT2(SCALE W12))OU6 (btTG PT3(SCALE PT3))OU7 (StrQ PT4(SCALF PT4))008 (SLTG CI(CAR PT1))00U9 (StTQ C2(CADI PTI))010 (StTU A(VD PT2 PT1))011 (S TU 8(VD PT4 Pi1))012 (StTU C(VD P13 PT2))013 (StTU U(VD PT3 PT4))014 (StTu P1(*QUO(DOT A(PERP D))015 (DUT C(PERP N)) ))016 (StTQ P2(*GUO(DOl C(PERP 9))017 (DOT C(PERP D)) ))018 (StTQ R3J(VSUM(SCALARPROD P1 PT2)A))019 (StTW R24(VSUM(SCALARPROD P2 PT4)7))020 (R.TURN(MAPCAR 'NELSONfLIST021 (CUAR 13)022 (CAR R24)023 C1024 (UAUR R13)025 (CAUR R24)026 C2027 P1028 P2))) ))EXPR)001002003 (DEFPROP PERP(LAMBDA(X)(LIST004 (CAUR X)005 (MINUS(CAR X)) ))EXPR)006007 (DEFPROP SCALE(LAMBDA(X)OU8 (SCALARPROD 16, X))EXPR)0U9010011 (DEFHROP VD(LAMBDA(X Y)(MAPCAR012 '*UIF013 X014 (VSUM Y '(0.0 0.0)) ))EXPP)015016 (DEFPRUP VSUM(LAMBDA(X Y)(MAPCAR017 'PLUS018 '(0.0 0.0)019 X020 Y))LXPR)021022 (DEFPROP DOT(LAMBDA(X Y)(EVAL023 (CONS 'PLUS(MAPCAR 'TIMES x Y))))EXPR)024025 (DEFPROP SCALARPROD(LAMBDA(X Y)(LIST026 (TIMES X 1.O(CAR Y))027 (TIMES X 1.0(CADR Y)) ))EXPR)028029 (DEFPROP NELSON(LAMBDA(X)(FIX0j0 (TIMES 1000000 X)))EXPR)0310J2033___(OPS MK(LSH -1000. 18.))(OPS HUNU(LSH 100. 18.))001002003004005006007008009010011012013014015016017018019020021022023(QUOTE REVERSE))1)7)0 3)0 3)NUMVAL)PARAMS 4)RT)PTABLE)NIL)(LAP VSCAN SUBR)(SYMBOLS 1(CALL 1(MOVE J(MOVEI 4HT (HLRZ 1(HRRZ 3(PUSHJ P(MOVeM I(SOJ6E 4(*VSCAN 0(MOVEI I(POPJ P)PTABLE (0 0(MK 0(HUND 0FARAMS (BLOCK 8.)ARY (BLOCK3)ARY)10.)1024.) 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How to Use .VSCAN

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How to Use .VSCAN

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