java - 求和面积表中的负和值(积分图像)

Question

我正在尝试在我的项目中实现积分图像概念(基于此解释 https://computersciencesource.wordpress.com/2010/09/03/computer-vision-the-integral-image/ )，但我遇到了一些问题。

我有一个带有双值的方(N * N)矩阵，我计算了相应的 SAT 表。下一步，我想知道值的总和从主对角线上的 R 索引开始，以正方形 block (L * L) 为单位。我不知道我是否可以解释得足够好让你理解，但我希望我的代码可以和你对话，比我更好;)

public class Testing {

    public Testing() {
        double[][] values = {
                            {0.00,0.00,0.00,0.00,0.00,0.00,3.95,4.35,1.92,12.07,14.16,134.88},
                            {0.00,0.00,0.00,0.00,0.00,0.00,0.00,4.74,1.13,12.23,5.70,89.01},
                            {0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,2.10,13.72,1.49,71.94},
                            {0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,7.58,7.79,55.21},
                            {0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,7.79,33.01},
                            {0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,3.92},
                            {5.39,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,22.09},
                            {9.34,0.39,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,37.28},
                            {5.79,4.35,3.23,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,47.29},
                            {5.67,3.82,0.97,6.30,0.00,0.00,0.00,0.00,0.00,0.00,0.00,47.29},
                            {24.11,6.31,6.45,13.88,0.00,0.00,0.00,0.00,0.00,0.00,0.00,47.29},
                            {46.09,69.39,55.13,46.03,41.76,7.00,31.91,43.70,58.39,98.75,132.71,0.00}
                            };

        double[][] sat = calculateSAT(values);
        int size = sat.length;

        for (int r = 0; r < size; r++) {
            System.out.println("R: " + r);
            for (int l = 2; l <= size - r; l++) {
                int blockSize = l - 1;
                double s_A, s_B, s_C, s_D = sat[r + blockSize][r + blockSize];

                if (r == 0) {
                    s_A = 0;
                    s_B = 0;
                    s_C = 0;
                }
                else {
                    s_A = sat[r - 1][r - 1];
                    s_B = sat[r + blockSize][r - 1];
                    s_C = sat[r - 1][r + blockSize];
                }

                System.out.println("L: " + l);
                System.out.println("Sum: " + (s_A + s_D - s_B - s_C));
            }
            System.out.println("-------------");
        }
    }

    public double[][] calculateSAT(double[][] matrix) {
        int size = matrix.length;
        double[][] sat = new double[size][size];

        for (int x = 0; x < size; x++) {
            for (int y = 0; y < size; y++) {
                double ixy = matrix[x][y], sat_left = 0.0, sat_top = 0.0, sat_lefttop = 0.0;
                if (x == 0) {
                    sat_left = 0;
                    sat_lefttop = 0;
                }
                else {
                    sat_left = sat[x-1][y];
                }
                if (y == 0) {
                    sat_top = 0;
                    sat_lefttop = 0;
                }
                else {
                    sat_top = sat[x][y-1];
                }
                if (x != 0 && y != 0) {
                    sat_lefttop = sat[x-1][y-1];
                }

                sat[x][y] = ixy + sat_left + sat_top - sat_lefttop;
            }
        }
        printSAT(sat);
        return sat;
    }

    public void printSAT(double[][] sat) {
        for (int x = 0; x < sat.length; x++) {
            for (int y = 0; y < sat.length; y++) {
                System.out.print(sat[x][y] + "\t");
            }
            System.out.println();
        }
        System.out.println("-------------");
    }

    public static void main(String[] args) {
        new Testing();
        System.out.println("All done! :D");
    }
}

输出是这样的:

0.0 0.0 0.0 0.0 0.0 0.0 3.95    8.3 10.22   22.29   36.45   171.32999999999998  
0.0 0.0 0.0 0.0 0.0 0.0 3.95    13.040000000000003  16.090000000000003  40.39   60.25000000000001   284.14  
0.0 0.0 0.0 0.0 0.0 0.0 3.95    13.040000000000003  18.190000000000005  56.21000000000001   77.56000000000002   373.39  
0.0 0.0 0.0 0.0 0.0 0.0 3.95    13.040000000000003  18.190000000000005  63.79000000000001   92.93000000000004   443.96999999999997  
0.0 0.0 0.0 0.0 0.0 0.0 3.95    13.040000000000003  18.190000000000005  63.79000000000001   100.72000000000003  484.77  
0.0 0.0 0.0 0.0 0.0 0.0 3.95    13.040000000000003  18.190000000000005  63.79000000000001   100.72000000000003  488.69000000000005  
5.39    5.39    5.39    5.39    5.39    5.39    9.34    18.430000000000003  23.580000000000002  69.18   106.11000000000001  516.1700000000001   
14.73   15.119999999999997  15.119999999999997  15.119999999999997  15.119999999999997  15.119999999999997  19.069999999999997  28.16   33.31   78.91000000000001   115.84000000000003  563.1800000000001   
20.52   25.259999999999994  28.489999999999995  28.489999999999995  28.489999999999995  28.489999999999995  32.43999999999999   41.53   46.68000000000001   92.28000000000002   129.21000000000004  623.84  
26.189999999999998  34.75   38.95   45.25   45.25   45.25   49.2    58.29000000000001   63.440000000000026  109.04000000000002  145.97000000000003  687.89  
50.3    65.17   75.82000000000001   96.00000000000001   96.0    96.0    99.94999999999999   109.04  114.19  159.79  196.71999999999997  785.9299999999998   
96.39   180.64999999999998  246.43  312.64000000000004  354.40000000000003  361.40000000000003  397.26  450.05  513.59  657.94  827.58  1416.7899999999997  
-------------
R: 0
L: 2
Sum: 0.0
L: 3
Sum: 0.0
L: 4
Sum: 0.0
L: 5
Sum: 0.0
L: 6
Sum: 0.0
L: 7
Sum: 9.34
L: 8
Sum: 28.16
L: 9
Sum: 46.68000000000001
L: 10
Sum: 109.04000000000002
L: 11
Sum: 196.71999999999997
L: 12
Sum: 1416.7899999999997
-------------
R: 1
L: 2
Sum: 0.0
L: 3
Sum: 0.0
L: 4
Sum: 0.0
L: 5
Sum: 0.0
L: 6
Sum: 0.0
L: 7
Sum: 5.129999999999999
L: 8
Sum: 15.940000000000007
L: 9
Sum: 60.560000000000024
L: 10
Sum: 109.96999999999996
L: 11
Sum: 1149.0699999999997
-------------
R: 2
L: 2
Sum: 0.0
L: 3
Sum: 0.0
L: 4
Sum: 0.0
L: 5
Sum: 0.0
L: 6
Sum: 0.0
L: 7
Sum: 5.330000000000009
L: 8
Sum: 33.90000000000002
L: 9
Sum: 71.29999999999995
L: 10
Sum: 951.9999999999999
-------------
R: 3
L: 2
Sum: 0.0
L: 3
Sum: 0.0
L: 4
Sum: 0.0
L: 5
Sum: 0.0
L: 6
Sum: 7.105427357601002E-15
L: 7
Sum: 13.88000000000001
L: 8
Sum: 43.33999999999995
L: 9
Sum: 796.9699999999997
-------------
R: 4
L: 2
Sum: 0.0
L: 3
Sum: 0.0
L: 4
Sum: 0.0
L: 5
Sum: 7.105427357601002E-15
L: 6
Sum: 7.105427357601002E-15
L: 7
Sum: 7.789999999999921
L: 8
Sum: 660.1799999999996
-------------
R: 5
L: 2
Sum: 0.0
L: 3
Sum: 0.0
L: 4
Sum: 7.105427357601002E-15
L: 5
Sum: 7.105427357601002E-15
L: 6
Sum: -5.6843418860808015E-14
L: 7
Sum: 577.6199999999997
-------------
R: 6
L: 2
Sum: 0.0
L: 3
Sum: 7.105427357601002E-15
L: 4
Sum: 7.105427357601002E-15
L: 5
Sum: -5.6843418860808015E-14
L: 6
Sum: 566.6999999999996
-------------
R: 7
L: 2
Sum: 1.7763568394002505E-14
L: 3
Sum: 1.4210854715202004E-14
L: 4
Sum: -2.8421709430404007E-14
L: 5
Sum: 512.6999999999996
-------------
R: 8
L: 2
Sum: -1.4210854715202004E-14
L: 3
Sum: -7.105427357601002E-14
L: 4
Sum: 431.7199999999998
-------------
R: 9
L: 2
Sum: -5.6843418860808015E-14
L: 3
Sum: 326.03999999999974
-------------
R: 10
L: 2
Sum: 179.99999999999966
-------------
R: 11
-------------
All done! :D

我对这段代码遇到的问题是其中一些总和是负数。那可能吗？如果我正确理解 SAT 表格，那应该是不可能的。

由于这些值非常小，这是 double 问题吗？

非常感谢您的帮助:)

PS:很抱歉我的英语没有比这更好。

Answer 1

是的，负值是由于精度问题造成的。如果数字足够小，则将其视为零。