灰度極座標的直方圖，可以比較方便的看到灰度的分佈圖，直觀的看出瞳孔、虹膜邊緣特點

虹膜的256灰度圖如下：

經過極座標的直方圖轉換後，如果如下：

100個點，64灰度直方圖

200點，32灰度直方圖

400點，32灰度直方圖

通過對比，可以看出，用32灰度的瞳孔灰度集中度非常高，一致性很好；

邊緣效果上，點數越多，識別的效果越精細，400點的邊緣識別越準確。

再給出400點的平均灰度直方圖的結果：

直觀的看出影象以圓點為中心，顏色越來越明亮；

分別對6張不同虹膜圖片的進行直方圖計算，原圖如下：

對應的直方圖計算結果如下：

參考程式碼如下：

void GenPlaneHistogram() {
        PlaneHistogram planeHistogram = new PlaneHistogram();
        int c = 100;  //可取不同的值，看到不同的效果100/200/400等
        int count[] = new int[c + 1];
        int countgray[][] = new int[c + 1][(int) (px * py / (Math.sqrt(c)))];
        int countgraymax[] = new int[c + 1];
        int countgraymaxgray[] = new int[c + 1];
        int countgraymaxratio[] = new int[c + 1];
        String text[] = new String[c + 1];
        Color color[] = new Color[c + 1];

        //找出半徑最大值，根據半徑按照100等分顯示
        double maxr = 0;
        double rr = 0;
        for (int i = 0; i < px; i++) {
            for (int j = 0; j < py; j++) {
                if (pixelpolar[i][j] > maxr) {
                    maxr = pixelpolar[i][j];
                }
            }
        }
        rr = maxr / c;
        System.out.println("maxr=" + maxr + ", rr=" + rr);
        //找出各段的計數
        int cc;
        for (int i = 0; i < px; i++) {
            for (int j = 0; j < py; j++) {
                cc = (int) (pixelpolar[i][j] / rr);
                countgray[cc][count[cc]] = pixelgray[i][j];
                count[cc]++;
            }
        }
        float bb;
        for (int i = 0; i < c + 1; i++) {
//            System.out.println("count[" + i + "]=" + count[i]);
            //尋找該區域灰度最大值
            //分為32個灰度區   (可取不同的值，看不同的效果，如64，128，256等，有三處地方需要修改，注意！)
            int countgraycount[] = new int[32];
            for (int j = 0; j < count[i]; j++) {                
//                System.out.println("countgray[" + j + "]=" + countgray[i][j]);
                countgraycount[countgray[i][j]/8]++;
            }
            countgraymax[i] = 0;
            for (int j = 0; j < 32; j++) {
//                System.out.println("countgraycount[" + j + "]=" + countgraycount[j]);
                if (countgraymax[i] < countgraycount[j])
                {
                    countgraymax[i] = countgraycount[j];
                    countgraymaxgray[i] = j;
//                    System.out.println("111 [" + i + "]=" + countgraymax[i] + "," + countgraymaxgray[i]);
                }
            }
            
            countgraymaxratio[i] = countgraymax[i]*100/count[i];
//            System.out.println("222 [" + i + "]=" + countgraymax[i] + "," + countgraymaxgray[i]);
        }
        for (int i = 0; i < c + 1; i++) {
            bb = (float) (Math.round(rr * i * 100)) / 100;
            text[i] = bb + "";
            color[i] = Color.GREEN;
        }
        //極座標半徑直方圖
        BufferedImage image = planeHistogram.paintPlaneHistogram("極座標半徑直方圖", count, text, color);
        File output = new File("111.jpg");
        try {
            ImageIO.write(image, "jpg", output);
        } catch (IOException e) {
            e.printStackTrace();
        }
        for (int i = 0; i < c + 1; i++) {
            text[i] = countgraymaxgray[i] + "";
            color[i] = Color.GREEN;
        }
        //灰度極座標的直方圖，X軸是極座標，Y軸是對應灰度密集區最大值的灰度值        
        BufferedImage image2 = planeHistogram.paintPlaneHistogram("灰度極座標直方圖", countgraymaxratio, text, color);
        File output2 = new File("222.jpg");
        try {
            ImageIO.write(image2, "jpg", output2);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }