private Line2 FitSimilarLine(List <Line2> lines, Line2 target, double angle = 20)
    {
        NumericalRecipes.RansacLine2d rcl = new NumericalRecipes.RansacLine2d();
        List <Vector2> linepoints         = new List <Vector2>();

        linepoints.AddRange(target.SamplePoints());
        //ransac
        for (int i = 0; i < lines.Count; i++)
        {
            if (Line2.IsParallel(lines[i], target, angle))
            {
                if (target.DistanceToLine(lines[i].start) < 30 && target.DistanceToLine(lines[i].end) < 30)
                {
                    linepoints.AddRange(lines[i].SamplePoints());
                }
            }
        }
        Line2 bestline = rcl.Estimate(linepoints);

        if (bestline == null)
        {
            return(target);
        }
        if (Vector2.Dot(bestline.dir, target.dir) < 0)
        {
            bestline.Flip();
        }
        return(bestline);
    }
    private Line2 FitCloseLine(List <Line2> lines, Line2 target, double dis = 30)
    {
        List <Vector2> linepoints = new List <Vector2>();

        linepoints.AddRange(target.SamplePoints());
        //ransac
        for (int i = 0; i < lines.Count; i++)
        {
            if (Line2.IsParallel(lines[i], target, 45))
            {
                double d = double.MaxValue;
                foreach (Vector2 v in linepoints)
                {
                    d = Math.Min(Math.Min(Vector2.Distance(lines[i].start, v), Vector2.Distance(lines[i].end, v)), d);
                }
                if (d < dis)
                {
                    linepoints.AddRange(lines[i].SamplePoints());
                }
            }
        }

        // least square
        //Vector2 dir = Utility.GetDirection(linepoints);
        //Line2 bestline = new Line2(linepoints[0], dir, true);
        //foreach (Vector2 v in linepoints)
        //    bestline.UpdateEnd(v);

        //ransac
        NumericalRecipes.RansacLine2d rcl = new NumericalRecipes.RansacLine2d();
        Line2 bestline = rcl.Estimate(linepoints);

        if (bestline == null)
        {
            return(target);
        }

        if (Vector2.Dot(bestline.dir, target.dir) < 0)
        {
            bestline.Flip();
        }
        return(bestline);
    }
    private List <Vector2> ApproximateStraightAxis(List <Line2> skel_lines)
    {
        // from skeleton lines(aka. thining image lines) (find lines that have the same direction with guessed axis <- when top face is known)
        // ransac, fit one line as main axis
        // update end points
        // set top circle center as start point
        // extend end point

        Line2             new_main_axis = null;
        Image <Rgb, byte> mainaxis_img  = body_img.Copy().Convert <Rgb, byte>();

        Line2 main_axis = null;

        if (iscube)
        {
            main_axis = ApproximateFromCubeTop();
        }
        else
        {
            main_axis = ApproximateFromTop();
        }

        if (main_axis == null)
        {
            return(null);
        }

        if (noface)
        {
            NumericalRecipes.RansacLine2d rcl = new NumericalRecipes.RansacLine2d();
            List <Vector2> thin_points        = IExtension.GetMaskPoints(this.ori_thin_img);
            List <Vector2> linepoints         = new List <Vector2>();
            for (int i = 0; i < skel_lines.Count; i++)
            {
                linepoints.AddRange(skel_lines[i].SamplePoints());
            }
            //Line2 bestline = rcl.Estimate(linepoints);
            Line2  bestline = rcl.Estimate(thin_points);
            double diss     = Vector2.Distance(bestline.start, face_center[0]);
            double dise     = Vector2.Distance(bestline.end, face_center[0]);
            if (dise < diss)
            {
                bestline.Flip();
            }
            new_main_axis = bestline;
        }
        else
        {
            // use ori thinning image as guidance
            LineSegment2D[] lines = ori_thin_img.HoughLinesBinary(
                1,               //Distance resolution in pixel-related units
                Math.PI / 180.0, //Angle resolution measured in radians.
                3,               //threshold
                4,               //min Line width
                1                //gap between lines
                )[0];            //Get the lines from the first channel

            skel_lines.Clear();
            foreach (LineSegment2D line in lines)
            {
                skel_lines.Add(new Line2(new Vector2(line.P1.X, line.P1.Y), new Vector2(line.P2.X, line.P2.Y)));
            }

            Line2 bestline = FitSimilarLine(skel_lines, main_axis);
            if (Line2.IsParallel(bestline, main_axis, 5))
            {
                new_main_axis = bestline;
            }
            else
            {
                new_main_axis = main_axis;
            }
        }

        // update end
        List <Vector2> ori_skel_points = IExtension.GetMaskPoints(ori_thin_img);

        for (int i = 0; i < ori_skel_points.Count; i++)
        {
            new_main_axis.UpdateEnd(ori_skel_points[i]);
        }
        new_main_axis.start = new_main_axis.ProjToLine(face_center.First());
        new_main_axis.start = new_main_axis.GetPointwithT(4);

        List <Vector2> axis_points = new List <Vector2>();

        // axis_points.Add(face_center.First());
        axis_points.AddRange(new_main_axis.SamplePoints());
        axis_points.Add(new_main_axis.GetPointwithT((float)new_main_axis.Length() * 1.2f));
        axis_points = IExtension.ResetPath(axis_points, 3);

        #region visualize
        Image <Rgb, byte> mainaxis_point_img = body_img.Copy().Convert <Rgb, byte>();
        foreach (Vector2 v in axis_points)
        {
            mainaxis_point_img.Draw(new CircleF(new PointF(v.x, v.y), 2.0f), new Rgb(255, 0, 0), 1);
        }
        mainaxis_point_img.Draw(new CircleF(new PointF(axis_points.First().x, axis_points.First().y), 3.0f), new Rgb(0, 255, 0), 1);
        mainaxis_point_img.Save(index_forname.ToString() + this.label_forname.ToString() + "_axis_straight.png");
        #endregion

        return(axis_points);
    }
    private List <Line2> Skeletonize(out bool iscurve)
    {
        Image <Gray, byte> img2   = body_img.Copy();
        Image <Gray, byte> eroded = new Image <Gray, byte>(img2.Size);
        Image <Gray, byte> temp   = new Image <Gray, byte>(img2.Size);
        Image <Gray, byte> skel   = new Image <Gray, byte>(img2.Size);

        body_img.Save("test.png");


        #region with matlab
        string argument1 = "\"" + "test.png" + "\"";
        System.Diagnostics.Process process = new System.Diagnostics.Process();
        process.StartInfo.FileName               = System.Environment.CurrentDirectory + "\\Assets\\frommatlab\\skeleton.exe";
        process.StartInfo.Arguments              = argument1;
        process.StartInfo.UseShellExecute        = false;
        process.StartInfo.CreateNoWindow         = true;
        process.StartInfo.RedirectStandardOutput = true;
        //启动
        process.Start();
        process.WaitForExit();
        #endregion

        skel          = new Image <Gray, byte>("prune.png");
        ori_thin_img  = new Image <Gray, byte>("thin.png");
        ori_prune_img = skel;

        #region thining - comment
        //skel.SetValue(0);
        //CvInvoke.Threshold(img2, temp, 127, 256, 0);
        //var element = CvInvoke.GetStructuringElement(ElementShape.Cross, new Size(3, 3), new Point(-1, -1));
        //bool done = false;

        ////skeleton
        //int itr = 0;
        //while (!done)
        //{
        //    CvInvoke.Erode(img2, eroded, element, new Point(-1, -1), 1, BorderType.Reflect, default(MCvScalar));
        //    CvInvoke.Dilate(eroded, temp, element, new Point(-1, -1), 1, BorderType.Reflect, default(MCvScalar));
        //    CvInvoke.Subtract(img2, temp, temp);
        //    CvInvoke.BitwiseOr(skel, temp, skel);
        //    eroded.CopyTo(img2);
        //    itr++;
        //    if (CvInvoke.CountNonZero(img2) == 0) done = true;
        //}
        //Image<Gray, Byte> cannyimg = body_img.Canny(60, 100);
        //CvInvoke.Dilate(cannyimg, cannyimg, element, new Point(-1, -1), 3, BorderType.Reflect, default(MCvScalar));
        //CvInvoke.Subtract(skel, cannyimg, skel);
        //ori_skel_img = skel.Copy();

        ////thinning
        //if (!noface)
        //{
        //    #region thinning
        //    List<Mat> cs = new List<Mat>();
        //    List<Mat> ds = new List<Mat>();
        //    for (int i = 0; i < 8; i++)
        //    {
        //        cs.Add(CvInvoke.GetStructuringElement(ElementShape.Cross, new Size(3, 3), new Point(-1, -1)));
        //        ds.Add(CvInvoke.GetStructuringElement(ElementShape.Cross, new Size(3, 3), new Point(-1, -1)));
        //    }

        //    cs[0].SetTo(new int[] { 0, 0, 0, 0, 1, 0, 1, 1, 1 });
        //    cs[1].SetTo(new int[] { 1, 0, 0, 1, 1, 0, 1, 0, 0 });
        //    cs[2].SetTo(new int[] { 1, 1, 1, 0, 1, 0, 0, 0, 0 });
        //    cs[3].SetTo(new int[] { 0, 0, 1, 0, 1, 1, 0, 0, 1 });

        //    ds[0].SetTo(new int[] { 1, 1, 1, 0, 0, 0, 0, 0, 0 });
        //    ds[1].SetTo(new int[] { 0, 0, 1, 0, 0, 1, 0, 0, 1 });
        //    ds[2].SetTo(new int[] { 0, 0, 0, 0, 0, 0, 1, 1, 1 });
        //    ds[3].SetTo(new int[] { 1, 0, 0, 1, 0, 0, 1, 0, 0 });

        //    cs[4].SetTo(new int[] { 0, 0, 0, 1, 1, 0, 1, 1, 0 });
        //    cs[5].SetTo(new int[] { 1, 1, 0, 1, 1, 0, 0, 0, 0 });
        //    cs[6].SetTo(new int[] { 0, 1, 1, 0, 1, 1, 0, 0, 0 });
        //    cs[7].SetTo(new int[] { 0, 0, 0, 0, 1, 1, 0, 1, 1 });

        //    ds[4].SetTo(new int[] { 0, 1, 1, 0, 0, 1, 0, 0, 0 });
        //    ds[5].SetTo(new int[] { 0, 0, 0, 0, 0, 1, 0, 1, 1 });
        //    ds[6].SetTo(new int[] { 0, 0, 0, 1, 0, 0, 1, 1, 0 });
        //    ds[7].SetTo(new int[] { 1, 1, 0, 1, 0, 0, 0, 0, 0 });

        //    Image<Gray, byte> img3 = skel.Copy();
        //    Image<Gray, byte> temp2 = skel.CopyBlank();
        //    Image<Gray, byte> lastimg3 = skel.Copy();

        //    done = false;
        //    while (!done)
        //    {
        //        for (int i = 0; i < 8; i++)
        //        {
        //            temp = this.HitOrMiss(img3, cs[i], ds[i]);
        //            CvInvoke.Subtract(img3, temp, img3);
        //        }

        //        CvInvoke.Subtract(lastimg3, img3, temp2);
        //        lastimg3 = img3.Copy();
        //        if (CvInvoke.CountNonZero(temp2) == 0) done = true;
        //    }

        //    //img3.Save("thining.png");
        //    #endregion
        //    skel = img3.Copy();
        //    ori_thinning_img = img3.Copy();
        //}
        ////// remove noise
        ////for (int i = 0; i < img3.Height; i++)
        ////{
        ////    for (int j = 0; j < img3.Width; j++)
        ////    {
        ////        if (img3[i, j].Equals(new Gray(255)))
        ////        {
        ////            bool change = false;
        ////            for (int pad = 1; pad < 3; pad++)
        ////            {
        ////                if (i >= pad && i < img3.Height - pad && j >= pad && j < img3.Width - pad)
        ////                {
        ////                    if (img3[i - pad, j].Equals(new Gray(0)) &&
        ////                        img3[i - pad, j - pad].Equals(new Gray(0)) &&
        ////                        img3[i - pad, j + pad].Equals(new Gray(0)) &&
        ////                        img3[i + pad, j].Equals(new Gray(0)) &&
        ////                        img3[i + pad, j - pad].Equals(new Gray(0)) &&
        ////                        img3[i + pad, j + pad].Equals(new Gray(0)) &&
        ////                        img3[i, j - pad].Equals(new Gray(0)) &&
        ////                        img3[i, j + pad].Equals(new Gray(0)))
        ////                        change = true;
        ////                }
        ////            }
        ////            if (change)
        ////                img3[i, j] = new Gray(0);
        ////        }
        ////    }
        ////}
        ////img3.Save("thiningdenoise.png");
        #endregion

        // get line
        // consider both straight line and curve
        LineSegment2D[] lines = skel.HoughLinesBinary(
            1,               //Distance resolution in pixel-related units
            Math.PI / 180.0, //Angle resolution measured in radians.
            3,               //threshold
            4,               //min Line width
            1                //gap between lines
            )[0];            //Get the lines from the first channel

        Image <Gray, byte> lineimg    = skel.CopyBlank();
        List <Line2>       skel_lines = new List <Line2>();
        foreach (LineSegment2D line in lines)
        {
            //remove image boundaries
            //if (line.P1.X > 10 && line.P1.Y > 10 && line.P1.X < body_img.Height - 10 && line.P1.Y < body_img.Width &&
            //   line.P2.X > 10 && line.P2.Y > 10 && line.P2.X < body_img.Height - 10 && line.P2.Y < body_img.Width - 10)
            //{
            skel_lines.Add(new Line2(new Vector2(line.P1.X, line.P1.Y), new Vector2(line.P2.X, line.P2.Y)));
            lineimg.Draw(line, new Gray(255), 2);
            //}
        }
        if (debug)
        {
            lineimg.Save("skel-line.png");
        }


        // cluster according to direction and relative distance
        // too many cluster means curve axis
        IMGSIZE = Math.Min(body_img.Width, body_img.Height);
        if (skel_lines.Count > 0)
        {
            double[][] xy = new double[skel_lines.Count][];
            for (int i = 0; i < skel_lines.Count; i++)
            {
                xy[i] = new double[] { skel_lines[i].start.x, skel_lines[i].start.y,
                                       skel_lines[i].end.x, skel_lines[i].end.y };
            }

            MeanShift clusterMS = new MeanShift(4, new UniformKernel(), 0.02);
            clusterMS.Distance = new myDistanceClass();
            MeanShiftClusterCollection clustering = clusterMS.Learn(xy);
            var lineLabels   = clustering.Decide(xy);
            int clustercount = lineLabels.DistinctCount();
            //Debug.Log("cluster count: " + clustercount);

            if (debug)
            {
                Image <Rgb, byte> lineimg_rgb = lineimg.Convert <Rgb, byte>();
                System.Random     rnd         = new System.Random();
                Rgb[]             colortable  = new Rgb[clustering.Count];
                for (int i = 0; i < clustering.Count; i++)
                {
                    colortable[i] = new Rgb(rnd.Next(255), rnd.Next(255), rnd.Next(255));
                }

                for (int i = 0; i < skel_lines.Count; i++)
                {
                    int label = lineLabels[i];
                    lineimg_rgb.Draw(skel_lines[i].ToLineSegment2D(), colortable[label], 2);
                }
                lineimg_rgb.Save("skel-line-cluster.png");
            }


            if (noface)
            {
                thred = 2;   // 2
            }
            if (clustercount > thred)
            {
                iscurve = true;
            }
            else
            {
                iscurve = false;
            }
        }
        else
        {
            iscurve = false;
            NumericalRecipes.RansacLine2d rcl = new NumericalRecipes.RansacLine2d();
            List <Vector2> linepoints         = new List <Vector2>();
            linepoints = IExtension.GetMaskPoints(skel);
            Line2 bestline = rcl.Estimate(linepoints);
            skel_lines.Add(bestline);
        }

        return(skel_lines);
    }