approx_chain🔗
Short description🔗
approx_chain — Approximate a contour by arcs and lines.
Warning🔗
approx_chain is obsolete and is only provided for
reasons of backward compatibility.
Signature🔗
approx_chain( point.y Row, point.x Column, real MinWidthCoord, real MaxWidthCoord, real ThreshStart, real ThreshEnd, real ThreshStep, real MinWidthSmooth, real MaxWidthSmooth, integer MinWidthCurve, integer MaxWidthCurve, real Weight1, real Weight2, real Weight3, out arc.center.y ArcCenterRow, out arc.center.x ArcCenterCol, out arc.angle.rad ArcAngle, out arc.begin.y ArcBeginRow, out arc.begin.x ArcBeginCol, out line.begin.y LineBeginRow, out line.begin.x LineBeginCol, out line.end.y LineEndRow, out line.end.x LineEndCol, out integer 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🔗
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🔗
Row (input_control) point.y-array → (integer)
Row of the contour.
Default: 32
Column (input_control) point.x-array → (integer)
Column of the contour.
Default: 32
MinWidthCoord (input_control) real → (real)
Minimum width of Gauss operator for coordinate smoothing (\(>\) 0.4).
Default: 0.5
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Value range: 0.4 ≤ MinWidthCoord ≤ 3.0 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
MaxWidthCoord (input_control) real → (real)
Maximum width of Gauss operator for coordinate smoothing (\(>\) 0.4).
Default: 2.4
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Value range: 0.4 ≤ MaxWidthCoord ≤ 3.0 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
ThreshStart (input_control) real → (real)
Minimum threshold value of the curvature for accepting a corner (relative to the largest curvature present).
Default: 0.3
Suggested values: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
Value range: 0.1 ≤ ThreshStart ≤ 0.9 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
ThreshEnd (input_control) real → (real)
Maximum threshold value of the curvature for accepting a corner (relative to the largest curvature present).
Default: 0.9
Suggested values: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
Value range: 0.1 ≤ ThreshEnd ≤ 0.9 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
ThreshStep (input_control) real → (real)
Step width for threshold increase.
Default: 0.2
Suggested values: 0.3, 0.4, 0.5
Value range: 0.1 ≤ ThreshStep ≤ 0.9 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
MinWidthSmooth (input_control) real → (real)
Minimum width of Gauss operator for smoothing the curvature function (\(>\) 0.4).
Default: 0.5
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Value range: 0.4 ≤ MinWidthSmooth ≤ 3.0 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
MaxWidthSmooth (input_control) real → (real)
Maximum width of Gauss operator for smoothing the curvature function.
Default: 2.4
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Value range: 0.4 ≤ MaxWidthSmooth ≤ 3.0 (lin)
Minimum increment: 0.01
Recommended increment: 0.1
MinWidthCurve (input_control) integer → (integer)
Minimum width of curve area for curvature determination (\(>\) 0.4).
Default: 2
Suggested values: 2, 5, 7
Value range: 1 ≤ MinWidthCurve ≤ 12 (lin)
Minimum increment: 1
Recommended increment: 2
MaxWidthCurve (input_control) integer → (integer)
Maximum width of curve area for curvature determination.
Default: 12
Suggested values: 2, 5, 7
Value range: 1 ≤ MaxWidthCurve ≤ 20 (lin)
Minimum increment: 1
Recommended increment: 2
Weight1 (input_control) real → (real)
Weighting factor for approximation precision.
Default: 1.0
Suggested values: 0.0, 0.5, 1.0
Value range: 0.0 ≤ Weight1 ≤ 1.0 (lin)
Minimum increment: 0.1
Recommended increment: 0.5
Weight2 (input_control) real → (real)
Weighting factor for large segments.
Default: 1.0
Suggested values: 0.0, 0.5, 1.0
Value range: 0.0 ≤ Weight2 ≤ 1.0 (lin)
Minimum increment: 0.1
Recommended increment: 0.5
Weight3 (input_control) real → (real)
Weighting factor for small segments.
Default: 1.0
Suggested values: 0.0, 0.5, 1.0
Value range: 0.0 ≤ Weight3 ≤ 1.0 (lin)
Minimum increment: 0.1
Recommended increment: 0.5
ArcCenterRow (output_control) arc.center.y-array → (integer)
Row of the center of an arc.
ArcCenterCol (output_control) arc.center.x-array → (integer)
Column of the center of an arc.
ArcAngle (output_control) arc.angle.rad-array → (real)
Angle of an arc.
ArcBeginRow (output_control) arc.begin.y-array → (integer)
Row of the starting point of an arc.
ArcBeginCol (output_control) arc.begin.x-array → (integer)
Column of the starting point of an arc.
LineBeginRow (output_control) line.begin.y-array → (integer)
Row of the starting point of a line segment.
LineBeginCol (output_control) line.begin.x-array → (integer)
Column of the starting point of a line segment.
LineEndRow (output_control) line.end.y-array → (integer)
Row of the ending point of a line segment.
LineEndCol (output_control) line.end.x-array → (integer)
Column of the ending point of a line segment.
Order (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_chain returns the value 2 (H_MSG_TRUE) if the
parameters are correct. Otherwise an exception is raised.
Combinations with other operators🔗
Combinations
Possible predecessors
sobel_amp, edges_image, get_region_contour, threshold, hysteresis_threshold
Possible successors
set_line_width, disp_arc, disp_line
Alternatives
get_region_polygon, approx_chain_simple
See also
Module🔗
Foundation