approx_chainT_approx_chainApproxChainApproxChain (Operator)

Name

approx_chainT_approx_chainApproxChainApproxChain — Approximate a contour by arcs and lines.

Warning

approx_chainapprox_chainApproxChainApproxChainApproxChain is obsolete and is only provided for reasons of backward compatibility.

Signature

approx_chain( : : Row, Column, MinWidthCoord, MaxWidthCoord, ThreshStart, ThreshEnd, ThreshStep, MinWidthSmooth, MaxWidthSmooth, MinWidthCurve, MaxWidthCurve, Weight1, Weight2, Weight3 : ArcCenterRow, ArcCenterCol, ArcAngle, ArcBeginRow, ArcBeginCol, LineBeginRow, LineBeginCol, LineEndRow, LineEndCol, Order)

Description

The coordinates of a curve are approximated by a row of lines and arcs. The procedure tries values from a user-definable range for certain parameters. The limits of these ranges are explicitly stated in the parameter list of the function (MinWidthCoord ... MaxWidthCoord, ThreshStart ... ThreshEnd, MinWidthSmooth ... MaxWidthSmooth, MinWidthCurve ... MaxWidthCurve). Additionally, the step width for the parameter area of the threshold value for pointed corners has to be indicated (ThreshStep). By narrowing the covered areas the runtime of the calculation can be shortened, but the result may deteriorate.

The parameters Weight1, Weight2 and Weight3 indicate whether the desired weighting is placed more on precision of the approximation, obtaining as much large segments as possible or as few small segments as possible. Thus, for (Weight1,Weight2,Weight3) (1,0,0) creates a very precise approximation and (0,1,1) an approximation with as few large segments as possible.

The result of the procedure is returned separately as arcs and lines. If one is interested in the sequence of the segments the individual resulting elements can be read successively from the resulting tuples; the sequence can be taken from the return parameter order (0: next element is next line segment, 1: next element is next arc segment).

Attention

Contours which can possibly consist of only one segment should also be examined with a threshold maximum (ThreshEnd) > 1.0, because otherwise at least one “corner point” is determined in any case.

Execution Information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

RowRowRowRowrow (input_control) point.y-array → (integer)

Row of the contour.

Default value: 32

ColumnColumnColumnColumncolumn (input_control) point.x-array → (integer)

Column of the contour.

Default value: 32

MinWidthCoordMinWidthCoordMinWidthCoordMinWidthCoordminWidthCoord (input_control) real → (real)

Minimum width of Gauss operator for coordinate smoothing (> 0.4).

Default value: 0.5

Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7

Typical range of values: 0.4 ≤ MinWidthCoord MinWidthCoord MinWidthCoord MinWidthCoord minWidthCoord ≤ 3.0 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

MaxWidthCoordMaxWidthCoordMaxWidthCoordMaxWidthCoordmaxWidthCoord (input_control) real → (real)

Maximum width of Gauss operator for coordinate smoothing (> 0.4).

Default value: 2.4

Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7

Typical range of values: 0.4 ≤ MaxWidthCoord MaxWidthCoord MaxWidthCoord MaxWidthCoord maxWidthCoord ≤ 3.0 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

ThreshStartThreshStartThreshStartThreshStartthreshStart (input_control) real → (real)

Minimum threshold value of the curvature for accepting a corner (relative to the largest curvature present).

Default value: 0.3

Suggested values: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8

Typical range of values: 0.1 ≤ ThreshStart ThreshStart ThreshStart ThreshStart threshStart ≤ 0.9 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

ThreshEndThreshEndThreshEndThreshEndthreshEnd (input_control) real → (real)

Maximum threshold value of the curvature for accepting a corner (relative to the largest curvature present).

Default value: 0.9

Suggested values: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8

Typical range of values: 0.1 ≤ ThreshEnd ThreshEnd ThreshEnd ThreshEnd threshEnd ≤ 0.9 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

ThreshStepThreshStepThreshStepThreshStepthreshStep (input_control) real → (real)

Step width for threshold increase.

Default value: 0.2

Suggested values: 0.3, 0.4, 0.5

Typical range of values: 0.1 ≤ ThreshStep ThreshStep ThreshStep ThreshStep threshStep ≤ 0.9 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

MinWidthSmoothMinWidthSmoothMinWidthSmoothMinWidthSmoothminWidthSmooth (input_control) real → (real)

Minimum width of Gauss operator for smoothing the curvature function (> 0.4).

Default value: 0.5

Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7

Typical range of values: 0.4 ≤ MinWidthSmooth MinWidthSmooth MinWidthSmooth MinWidthSmooth minWidthSmooth ≤ 3.0 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

MaxWidthSmoothMaxWidthSmoothMaxWidthSmoothMaxWidthSmoothmaxWidthSmooth (input_control) real → (real)

Maximum width of Gauss operator for smoothing the curvature function.

Default value: 2.4

Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7

Typical range of values: 0.4 ≤ MaxWidthSmooth MaxWidthSmooth MaxWidthSmooth MaxWidthSmooth maxWidthSmooth ≤ 3.0 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

MinWidthCurveMinWidthCurveMinWidthCurveMinWidthCurveminWidthCurve (input_control) integer → (integer)

Minimum width of curve area for curvature determination (> 0.4).

Default value: 2

Suggested values: 2, 5, 7

Typical range of values: 1 ≤ MinWidthCurve MinWidthCurve MinWidthCurve MinWidthCurve minWidthCurve ≤ 12 (lin)

Minimum increment: 1

Recommended increment: 2

MaxWidthCurveMaxWidthCurveMaxWidthCurveMaxWidthCurvemaxWidthCurve (input_control) integer → (integer)

Maximum width of curve area for curvature determination.

Default value: 12

Suggested values: 2, 5, 7

Typical range of values: 1 ≤ MaxWidthCurve MaxWidthCurve MaxWidthCurve MaxWidthCurve maxWidthCurve ≤ 20 (lin)

Minimum increment: 1

Recommended increment: 2

Weight1Weight1Weight1Weight1weight1 (input_control) real → (real)

Weighting factor for approximation precision.

Default value: 1.0

Suggested values: 0.0, 0.5, 1.0

Typical range of values: 0.0 ≤ Weight1 Weight1 Weight1 Weight1 weight1 ≤ 1.0 (lin)

Minimum increment: 0.1

Recommended increment: 0.5

Weight2Weight2Weight2Weight2weight2 (input_control) real → (real)

Weighting factor for large segments.

Default value: 1.0

Suggested values: 0.0, 0.5, 1.0

Typical range of values: 0.0 ≤ Weight2 Weight2 Weight2 Weight2 weight2 ≤ 1.0 (lin)

Minimum increment: 0.1

Recommended increment: 0.5

Weight3Weight3Weight3Weight3weight3 (input_control) real → (real)

Weighting factor for small segments.

Default value: 1.0

Suggested values: 0.0, 0.5, 1.0

Typical range of values: 0.0 ≤ Weight3 Weight3 Weight3 Weight3 weight3 ≤ 1.0 (lin)

Minimum increment: 0.1

Recommended increment: 0.5

ArcCenterRowArcCenterRowArcCenterRowArcCenterRowarcCenterRow (output_control) arc.center.y-array → (integer)

Row of the center of an arc.

ArcCenterColArcCenterColArcCenterColArcCenterColarcCenterCol (output_control) arc.center.x-array → (integer)

Column of the center of an arc.

ArcAngleArcAngleArcAngleArcAnglearcAngle (output_control) arc.angle.rad-array → (real)

Angle of an arc.

ArcBeginRowArcBeginRowArcBeginRowArcBeginRowarcBeginRow (output_control) arc.begin.y-array → (integer)

Row of the starting point of an arc.

ArcBeginColArcBeginColArcBeginColArcBeginColarcBeginCol (output_control) arc.begin.x-array → (integer)

Column of the starting point of an arc.

LineBeginRowLineBeginRowLineBeginRowLineBeginRowlineBeginRow (output_control) line.begin.y-array → (integer)

Row of the starting point of a line segment.

LineBeginColLineBeginColLineBeginColLineBeginCollineBeginCol (output_control) line.begin.x-array → (integer)

Column of the starting point of a line segment.

LineEndRowLineEndRowLineEndRowLineEndRowlineEndRow (output_control) line.end.y-array → (integer)

Row of the ending point of a line segment.

LineEndColLineEndColLineEndColLineEndCollineEndCol (output_control) line.end.x-array → (integer)

Column of the ending point of a line segment.

OrderOrderOrderOrderorder (output_control) integer-array → (integer)

Sequence of line (value 0) and arc segments (value 1).

Example (C)

/* read edge image  */
read_image(&Image,"fig1_kan");
/* construct edge region  */
hysteresis_threshold(Image,&RK1,64,255,40,1);
connection(RK1,&Rand);
/* fetch chain code  */
T_get_region_contour(Rand,&Rows,&Columns);
firstline = get_i(Tline,0);
firstcol = get_i(Tcol,0);
/* approximation with lines and circular arcs */
set_d(t1,0.4,0);
set_d(t2,2.4,0);

set_d(t3,0.3,0);
set_d(t4,0.9,0);

set_d(t5,0.2,0);

set_d(t6,0.4,0);
set_d(t7,2.4,0);

set_i(t8,2,0);
set_i(t9,12,0);

set_d(t10,1.0,0);
set_d(t11,1.0,0);
set_d(t12,1.0,0);

T_approx_chain(Rows,Columns,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,
                &Bzl,&Bzc,&Br,&Bwl,&Bwc,&Ll0,&Lc0,&Ll1,&Lc1,&order);
nob = length_tuple(Bzl);
nol = length_tuple(Ll0);
/* draw lines and arcs */
set_i(WindowHandleTuple,WindowHandle,0);
set_line_width(WindowHandle,4);
if (nob>0) T_disp_arc(Bzl,Bzc,Br,Bwl,Bwc);
set_line_width(WindowHandle,1);
if (nol>0) T_disp_line(WindowHandleTuple,Ll0,Lc0,Ll1,Lc1);

Result

The operator approx_chainapprox_chainApproxChainApproxChainApproxChain returns the value 2 (H_MSG_TRUE) if the parameters are correct. Otherwise an exception is raised.