approx_chain

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 )

Approximate a contour by arcs and lines.

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.

Parameters

`Row` (input_control)	point.y `->` integer
Row of the contour.
Default value: 32

`Column` (input_control)	point.x `->` integer
Column of the contour.
Default value: 32

`MinWidthCoord` (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 <= 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 value: 2.4
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Typical range of values: `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 value: 0.3
Suggested values: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
Typical range of values: `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 value: 0.9
Suggested values: 0.3, 0.4, 0.5, 0.6, 0.7, 0.8
Typical range of values: `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 value: 0.2
Suggested values: 0.3, 0.4, 0.5
Typical range of values: `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 value: 0.5
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Typical range of values: `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 value: 2.4
Suggested values: 0.5, 0.7, 1.0, 1.2, 1.5, 1.7
Typical range of values: `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 value: 2
Suggested values: 2, 5, 7
Typical range of values: `1 <= MinWidthCurve <= 12` (lin)
Minimum increment: 1
Recommended increment: 2

`MaxWidthCurve` (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 <= 20` (lin)
Minimum increment: 1
Recommended increment: 2

`Weight1` (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 <= 1.0` (lin)
Minimum increment: 0.1
Recommended increment: 0.5

`Weight2` (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 <= 1.0` (lin)
Minimum increment: 0.1
Recommended increment: 0.5

`Weight3` (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 <= 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

/* 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.

Parallelization Information

approx_chain is reentrant and processed without parallelization.

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

Module

Region processing