Java implement cross correlation 2d image

Question

enter image description here

Can i implement the cross-correlation in the same way as the convolution?

I want to implement the formula in as in the picture, where Li the kernel in 4 different direction filters; Ci is the magnitude map for direction i. So what I did is to find the cross-correlation in the four directions separately and add them up. I learned that the cross correlation can be the same as convolution in image line sharping; s as the result should be stroke line of an image but what I actually get are discrete points. I am not sure if I implemented the formula correctly. Please help

private static void sharpTheLine(){
        int[][] cC_0= crossCorrelation(KERNEL_0,CMap_0);
        int[][] cC_45=crossCorrelation(KERNEL_45,CMap_45);
        int[][] cC_90=crossCorrelation(KERNEL_90,CMap_90);
        int[][] cC_135=crossCorrelation(KERNEL_135,CMap_135);


        //generate S
        for(int i=0; i<imageWidth; i++){
            for(int j =0; j<imageHight; j++) {
                SMap[i][j] = cC_0[i][j]+cC_45[i][j]+cC_90[i][j]+cC_135[i][j];
            }
        }
    }

    private static int[][] crossCorrelation(int [][] kernel,int[][] CMapVal){
        int horizontalWalk = imageWidth - K_R;
        int verticalWalk = imageHight - K_C;
        int res[][]=new int[imageWidth][imageHight];
        for (int i = 0; i < horizontalWalk; i++) {
            for (int j = 0; j < verticalWalk; j++) {
                int sample[][] = new int[K_R][K_C];
                for (int k = i; k < K_R + i; k++) {
                    for (int m = j; m < K_C + j; m++) {
                        sample[k - i][m - j] = CMapVal[k][m];
                        OnePixelConvolution(sample, i, j, kernel, res);
                    }
                }
            }
        }

        return res;
    }
private static void OnePixelConvolution(int[][] sample, int x, int y, int [][]kernel, int [][] res) {
        int resrgb = 0;
        for (int i = 0; i < K_R; i++) {
            for (int j = 0; j < K_C; j++) {
                resrgb = resrgb + sample[i][j] * kernel[i][j];
            }
        }
        res[x][y] = resrgb;
    }