How multiply convolutional core of 3x3 and an image

There is a convolutional core of 3x3 and an image represented by an array of pixels of integer values.

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A convolutional kernel is represented as follows:

//compound convolutional kernels
//                                | 1, 0,  1|
// convolutional kernel H = src x | 0, 0,  0|
//                                |-1, 0, -1|

//                                | 1, 0, -1|
// convolutional kernel V = src x | 0, 0,  0|
//                                | 1, 0, -1|

convolutional kernels = kernel H + kernel V

for(int inc=0; inc<height-2; inc++)
{
    //loaded 3 lines into memory
    str1_16pxs = _mm_loadu_si128((__m128i*)(src_all_str));
    str2_16pxs = _mm_loadu_si128((__m128i*)(src2_all_str));
    str3_16pxs = _mm_loadu_si128((__m128i*)(src3_all_str));

    //packing 16bit
    str1_16pxs_pack1st_8to16 = _mm_cvtepu8_epi16(str1_16pxs);
    str2_16pxs_pack1st_8to16 = _mm_cvtepu8_epi16(str2_16pxs);
    str3_16pxs_pack1st_8to16 = _mm_cvtepu8_epi16(str3_16pxs);

//---!
        //there is we make the first convolution for 8px's
        //... How ???
//---

    //summ 1st 8to16 vertical registers
    sum1_str12_vert_16pxs_pack1st_8to16  = _mm_add_epi16(str1_16pxs_pack1st_8to16,           str2_16pxs_pack1st_8to16);
    sum1_str123_vert_16pxs_pack1st_8to16 = _mm_add_epi16(sum1_str12_vert_16pxs_pack1st_8to16,str3_16pxs_pack1st_8to16);

    for(int jnc=0; jnc<(width >> 4); jnc++)
    {
        str1_16pxs_plus_8pxs = _mm_srli_si128(str1_16pxs, 8);
        str2_16pxs_plus_8pxs = _mm_srli_si128(str2_16pxs, 8);
        str3_16pxs_plus_8pxs = _mm_srli_si128(str3_16pxs, 8);

        //pack 2nd 8to16 registers (+8px's)
        str1_16pxs_pack2nd_8to16 = _mm_cvtepu8_epi16(str1_16pxs_plus_8pxs);
        str2_16pxs_pack2nd_8to16 = _mm_cvtepu8_epi16(str2_16pxs_plus_8pxs);
        str3_16pxs_pack2nd_8to16 = _mm_cvtepu8_epi16(str3_16pxs_plus_8pxs);

//---!
            //do convolution for the remaining 8px's and so on until the end of the read line
            //... How ???
//---

        //summ vertic 8to16 registers
        sum1_str12_vert_16pxs_pack2nd_8to16  = _mm_add_epi16(str1_16pxs_pack2nd_8to16,           str2_16pxs_pack2nd_8to16);
        sum1_str123_vert_16pxs_pack2nd_8to16 = _mm_add_epi16(sum1_str12_vert_16pxs_pack2nd_8to16,str3_16pxs_pack2nd_8to16);

//---!4     loading next 16 px's
        src_all_str += 16;
        src2_all_str += 16;
        src3_all_str += 16;

        //...

        _mm_store_si128((__m128i*)(dst_all_str), res);
        dst_all_str += 8;

    }//for(jnc)

}//for(inc)