-01-生成ORB离散查找表【特征点检测】

ORB算法计算描述子时需要使用到一个提前计算好的查找表，具体可以看OpenCV的orb.cpp文件中的数组：
static int bit_pattern_31_[256*4]

这个查找表对应的是0度，当特征点不是0度时，需要将查找表中的坐标进行旋转，这部分代码在OpenCV中有。再看论文中，作者将查找表以12°步进的方式生成了30个离散的查找表，这样计算时就能够快速选定坐标位置。

作者选的30等分角度应该是评估过误差的，我就先不去考虑了，而且我一时找不到包含这30个查找表的源码，所以只能手动生成了。

Python

一如既往用Python来做。
脚本还有相关的文件都在后面，粘贴保存后直接可用。

我把一对坐标信息，四个数值：x0,y0,x1,y1直接保存到了一个uint32类型当中去，并对各个数值进行了一个偏移（坐标旋转后最大边界会到达±18，所以偏移选了18，坐标所在的窗口为37*37）。
这样方便我后面在fpga对这些数据进行查表操作，嘻嘻··

要是大家有需求的话，把这个脚本稍微改一改就能得到自己想用到的格式了。

Python脚本文件：
bit_pattern_12degrees_inc.py

import mathdef char2int(n):    if n&0x80:        ret = -((~n&0xff)+1)    else:        ret = n    return retfile = open('bit_pattern_31_.txt', 'r')lines_int_array = []while 1:    lines = file.readlines(1000)    if not lines:        break    for line in lines:        line_str = line[:line.find('/*')]        line_str_array = line_str.split(',')        tmp = map(int, line_str_array)        lines_int_array.append(tmp)        pass#print lines_int_arrayprint '--------------'#disperse_incDINC = 12KERNEL = 31kernel_half = KERNEL/2#------------------------------------------max_num = 0;min_num = 0;max_rot = 0;for line_int_array in lines_int_array:    max_temp = max(line_int_array)    min_temp = min(line_int_array)    if(max_num < max_temp):        max_num = max_temp    if(min_num > min_temp):        min_num = min_tempif(abs(min_num) > abs(max_num)):    max_rot = abs(min_num)else:    max_rot = abs(min_num)max_offset = int(round(max_rot*math.cos(math.radians(45))+max_rot*math.sin(math.radians(45))))print 'max num = %d'%max_numprint 'min num = %d'%min_numprint 'max rot = %d'%max_rotprint 'max offset = %d'%max_offset#------------------------------------------file_dst = open('bit_pattern_12degrees_inc.c', 'w')file_dst.write('// Attention:\n')file_dst.write('// The look up table max offset is : ' + str(max_offset) + '\n')file_dst.write('// The image window is : ' + str(max_offset*2+1) + '^2\n')file_dst.write('\n\n ')for j in range(360/DINC):    lut_num_int_s = j*DINC-6    if(lut_num_int_s < 0):        lut_num_int_s += 360    lut_num_int_e = (j+1)*DINC-1-6    lut_num_str_s = str(lut_num_int_s)    lut_num_str_e = str(lut_num_int_e)    lut_num_str = lut_num_str_s + '_' + lut_num_str_e    file_dst.write('//lut from ' + lut_num_str_s + ' degree to ' + lut_num_str_e + ' degree.\n')    file_dst.write('unsigned int bit_pattern_' + str(max_offset*2+1) + '_unt32_' + str(j+1) + '_of' + str(360/DINC) + '[256] =\n{\n')    for i in range(len(lines_int_array)):        x0 = lines_int_array[i][0]        y0 = lines_int_array[i][1]        x1 = lines_int_array[i][2]        y1 = lines_int_array[i][3]        r_cos = math.cos(math.radians(DINC*j))        r_sin = math.sin(math.radians(DINC*j))        r_x0 = int(round(x0*r_cos - y0*r_sin))        r_y0 = int(round(x0*r_sin + y0*r_cos))        r_x1 = int(round(x1*r_cos - y1*r_sin))        r_y1 = int(round(x1*r_sin + y1*r_cos))        line_int32_offset = ((r_x0+max_offset)&0xff)<<0 | \                            ((r_y0+max_offset)&0xff)<<8 | \                            ((r_x1+max_offset)&0xff)<<16 | \                            ((r_y1+max_offset)&0xff)<<24        file_dst.write('\t')        file_dst.write('0x%08x'%line_int32_offset)        if(i == len(lines_int_array)-1):            file_dst.write(' ')        else:            file_dst.write(',')        file_dst.write(' //%3d,'%r_x0 + '%3d,'%r_y0 + '%3d,'%r_x1 + '%3d,'%r_y1 + ' ---%3d'%i)        file_dst.write('\n')    file_dst.write('};\n')    file_dst.write('\n')    file_dst.write('\n')file_dst.close()file.close()

数组文件：
bit_pattern_31_.txt

    8,-3, 9,5/*mean (0), correlation (0)*/,    4,2, 7,-12/*mean (1.12461e-05), correlation (0.0437584)*/,    -11,9, -8,2/*mean (3.37382e-05), correlation (0.0617409)*/,    7,-12, 12,-13/*mean (5.62303e-05), correlation (0.0636977)*/,    2,-13, 2,12/*mean (0.000134953), correlation (0.085099)*/,    1,-7, 1,6/*mean (0.000528565), correlation (0.0857175)*/,    -2,-10, -2,-4/*mean (0.0188821), correlation (0.0985774)*/,    -13,-13, -11,-8/*mean (0.0363135), correlation (0.0899616)*/,    -13,-3, -12,-9/*mean (0.121806), correlation (0.099849)*/,    10,4, 11,9/*mean (0.122065), correlation (0.093285)*/,    -13,-8, -8,-9/*mean (0.162787), correlation (0.0942748)*/,    -11,7, -9,12/*mean (0.21561), correlation (0.0974438)*/,    7,7, 12,6/*mean (0.160583), correlation (0.130064)*/,    -4,-5, -3,0/*mean (0.228171), correlation (0.132998)*/,    -13,2, -12,-3/*mean (0.00997526), correlation (0.145926)*/,    -9,0, -7,5/*mean (0.198234), correlation (0.143636)*/,    12,-6, 12,-1/*mean (0.0676226), correlation (0.16689)*/,    -3,6, -2,12/*mean (0.166847), correlation (0.171682)*/,    -6,-13, -4,-8/*mean (0.101215), correlation (0.179716)*/,    11,-13, 12,-8/*mean (0.200641), correlation (0.192279)*/,    4,7, 5,1/*mean (0.205106), correlation (0.186848)*/,    5,-3, 10,-3/*mean (0.234908), correlation (0.192319)*/,    3,-7, 6,12/*mean (0.0709964), correlation (0.210872)*/,    -8,-7, -6,-2/*mean (0.0939834), correlation (0.212589)*/,    -2,11, -1,-10/*mean (0.127778), correlation (0.20866)*/,    -13,12, -8,10/*mean (0.14783), correlation (0.206356)*/,    -7,3, -5,-3/*mean (0.182141), correlation (0.198942)*/,    -4,2, -3,7/*mean (0.188237), correlation (0.21384)*/,    -10,-12, -6,11/*mean (0.14865), correlation (0.23571)*/,    5,-12, 6,-7/*mean (0.222312), correlation (0.23324)*/,    5,-6, 7,-1/*mean (0.229082), correlation (0.23389)*/,    1,0, 4,-5/*mean (0.241577), correlation (0.215286)*/,    9,11, 11,-13/*mean (0.00338507), correlation (0.251373)*/,    4,7, 4,12/*mean (0.131005), correlation (0.257622)*/,    2,-1, 4,4/*mean (0.152755), correlation (0.255205)*/,    -4,-12, -2,7/*mean (0.182771), correlation (0.244867)*/,    -8,-5, -7,-10/*mean (0.186898), correlation (0.23901)*/,    4,11, 9,12/*mean (0.226226), correlation (0.258255)*/,    0,-8, 1,-13/*mean (0.0897886), correlation (0.274827)*/,    -13,-2, -8,2/*mean (0.148774), correlation (0.28065)*/,    -3,-2, -2,3/*mean (0.153048), correlation (0.283063)*/,    -6,9, -4,-9/*mean (0.169523), correlation (0.278248)*/,    8,12, 10,7/*mean (0.225337), correlation (0.282851)*/,    0,9, 1,3/*mean (0.226687), correlation (0.278734)*/,    7,-5, 11,-10/*mean (0.00693882), correlation (0.305161)*/,    -13,-6, -11,0/*mean (0.0227283), correlation (0.300181)*/,    10,7, 12,1/*mean (0.125517), correlation (0.31089)*/,    -6,-3, -6,12/*mean (0.131748), correlation (0.312779)*/,    10,-9, 12,-4/*mean (0.144827), correlation (0.292797)*/,    -13,8, -8,-12/*mean (0.149202), correlation (0.308918)*/,    -13,0, -8,-4/*mean (0.160909), correlation (0.310013)*/,    3,3, 7,8/*mean (0.177755), correlation (0.309394)*/,    5,7, 10,-7/*mean (0.212337), correlation (0.310315)*/,    -1,7, 1,-12/*mean (0.214429), correlation (0.311933)*/,    3,-10, 5,6/*mean (0.235807), correlation (0.313104)*/,    2,-4, 3,-10/*mean (0.00494827), correlation (0.344948)*/,    -13,0, -13,5/*mean (0.0549145), correlation (0.344675)*/,    -13,-7, -12,12/*mean (0.103385), correlation (0.342715)*/,    -13,3, -11,8/*mean (0.134222), correlation (0.322922)*/,    -7,12, -4,7/*mean (0.153284), correlation (0.337061)*/,    6,-10, 12,8/*mean (0.154881), correlation (0.329257)*/,    -9,-1, -7,-6/*mean (0.200967), correlation (0.33312)*/,    -2,-5, 0,12/*mean (0.201518), correlation (0.340635)*/,    -12,5, -7,5/*mean (0.207805), correlation (0.335631)*/,    3,-10, 8,-13/*mean (0.224438), correlation (0.34504)*/,    -7,-7, -4,5/*mean (0.239361), correlation (0.338053)*/,    -3,-2, -1,-7/*mean (0.240744), correlation (0.344322)*/,    2,9, 5,-11/*mean (0.242949), correlation (0.34145)*/,    -11,-13, -5,-13/*mean (0.244028), correlation (0.336861)*/,    -1,6, 0,-1/*mean (0.247571), correlation (0.343684)*/,    5,-3, 5,2/*mean (0.000697256), correlation (0.357265)*/,    -4,-13, -4,12/*mean (0.00213675), correlation (0.373827)*/,    -9,-6, -9,6/*mean (0.0126856), correlation (0.373938)*/,    -12,-10, -8,-4/*mean (0.0152497), correlation (0.364237)*/,    10,2, 12,-3/*mean (0.0299933), correlation (0.345292)*/,    7,12, 12,12/*mean (0.0307242), correlation (0.366299)*/,    -7,-13, -6,5/*mean (0.0534975), correlation (0.368357)*/,    -4,9, -3,4/*mean (0.099865), correlation (0.372276)*/,    7,-1, 12,2/*mean (0.117083), correlation (0.364529)*/,    -7,6, -5,1/*mean (0.126125), correlation (0.369606)*/,    -13,11, -12,5/*mean (0.130364), correlation (0.358502)*/,    -3,7, -2,-6/*mean (0.131691), correlation (0.375531)*/,    7,-8, 12,-7/*mean (0.160166), correlation (0.379508)*/,    -13,-7, -11,-12/*mean (0.167848), correlation (0.353343)*/,    1,-3, 12,12/*mean (0.183378), correlation (0.371916)*/,    2,-6, 3,0/*mean (0.228711), correlation (0.371761)*/,    -4,3, -2,-13/*mean (0.247211), correlation (0.364063)*/,    -1,-13, 1,9/*mean (0.249325), correlation (0.378139)*/,    7,1, 8,-6/*mean (0.000652272), correlation (0.411682)*/,    1,-1, 3,12/*mean (0.00248538), correlation (0.392988)*/,    9,1, 12,6/*mean (0.0206815), correlation (0.386106)*/,    -1,-9, -1,3/*mean (0.0364485), correlation (0.410752)*/,    -13,-13, -10,5/*mean (0.0376068), correlation (0.398374)*/,    7,7, 10,12/*mean (0.0424202), correlation (0.405663)*/,    12,-5, 12,9/*mean (0.0942645), correlation (0.410422)*/,    6,3, 7,11/*mean (0.1074), correlation (0.413224)*/,    5,-13, 6,10/*mean (0.109256), correlation (0.408646)*/,    2,-12, 2,3/*mean (0.131691), correlation (0.416076)*/,    3,8, 4,-6/*mean (0.165081), correlation (0.417569)*/,    2,6, 12,-13/*mean (0.171874), correlation (0.408471)*/,    9,-12, 10,3/*mean (0.175146), correlation (0.41296)*/,    -8,4, -7,9/*mean (0.183682), correlation (0.402956)*/,    -11,12, -4,-6/*mean (0.184672), correlation (0.416125)*/,    1,12, 2,-8/*mean (0.191487), correlation (0.386696)*/,    6,-9, 7,-4/*mean (0.192668), correlation (0.394771)*/,    2,3, 3,-2/*mean (0.200157), correlation (0.408303)*/,    6,3, 11,0/*mean (0.204588), correlation (0.411762)*/,    3,-3, 8,-8/*mean (0.205904), correlation (0.416294)*/,    7,8, 9,3/*mean (0.213237), correlation (0.409306)*/,    -11,-5, -6,-4/*mean (0.243444), correlation (0.395069)*/,    -10,11, -5,10/*mean (0.247672), correlation (0.413392)*/,    -5,-8, -3,12/*mean (0.24774), correlation (0.411416)*/,    -10,5, -9,0/*mean (0.00213675), correlation (0.454003)*/,    8,-1, 12,-6/*mean (0.0293635), correlation (0.455368)*/,    4,-6, 6,-11/*mean (0.0404971), correlation (0.457393)*/,    -10,12, -8,7/*mean (0.0481107), correlation (0.448364)*/,    4,-2, 6,7/*mean (0.050641), correlation (0.455019)*/,    -2,0, -2,12/*mean (0.0525978), correlation (0.44338)*/,    -5,-8, -5,2/*mean (0.0629667), correlation (0.457096)*/,    7,-6, 10,12/*mean (0.0653846), correlation (0.445623)*/,    -9,-13, -8,-8/*mean (0.0858749), correlation (0.449789)*/,    -5,-13, -5,-2/*mean (0.122402), correlation (0.450201)*/,    8,-8, 9,-13/*mean (0.125416), correlation (0.453224)*/,    -9,-11, -9,0/*mean (0.130128), correlation (0.458724)*/,    1,-8, 1,-2/*mean (0.132467), correlation (0.440133)*/,    7,-4, 9,1/*mean (0.132692), correlation (0.454)*/,    -2,1, -1,-4/*mean (0.135695), correlation (0.455739)*/,    11,-6, 12,-11/*mean (0.142904), correlation (0.446114)*/,    -12,-9, -6,4/*mean (0.146165), correlation (0.451473)*/,    3,7, 7,12/*mean (0.147627), correlation (0.456643)*/,    5,5, 10,8/*mean (0.152901), correlation (0.455036)*/,    0,-4, 2,8/*mean (0.167083), correlation (0.459315)*/,    -9,12, -5,-13/*mean (0.173234), correlation (0.454706)*/,    0,7, 2,12/*mean (0.18312), correlation (0.433855)*/,    -1,2, 1,7/*mean (0.185504), correlation (0.443838)*/,    5,11, 7,-9/*mean (0.185706), correlation (0.451123)*/,    3,5, 6,-8/*mean (0.188968), correlation (0.455808)*/,    -13,-4, -8,9/*mean (0.191667), correlation (0.459128)*/,    -5,9, -3,-3/*mean (0.193196), correlation (0.458364)*/,    -4,-7, -3,-12/*mean (0.196536), correlation (0.455782)*/,    6,5, 8,0/*mean (0.1972), correlation (0.450481)*/,    -7,6, -6,12/*mean (0.199438), correlation (0.458156)*/,    -13,6, -5,-2/*mean (0.211224), correlation (0.449548)*/,    1,-10, 3,10/*mean (0.211718), correlation (0.440606)*/,    4,1, 8,-4/*mean (0.213034), correlation (0.443177)*/,    -2,-2, 2,-13/*mean (0.234334), correlation (0.455304)*/,    2,-12, 12,12/*mean (0.235684), correlation (0.443436)*/,    -2,-13, 0,-6/*mean (0.237674), correlation (0.452525)*/,    4,1, 9,3/*mean (0.23962), correlation (0.444824)*/,    -6,-10, -3,-5/*mean (0.248459), correlation (0.439621)*/,    -3,-13, -1,1/*mean (0.249505), correlation (0.456666)*/,    7,5, 12,-11/*mean (0.00119208), correlation (0.495466)*/,    4,-2, 5,-7/*mean (0.00372245), correlation (0.484214)*/,    -13,9, -9,-5/*mean (0.00741116), correlation (0.499854)*/,    7,1, 8,6/*mean (0.0208952), correlation (0.499773)*/,    7,-8, 7,6/*mean (0.0220085), correlation (0.501609)*/,    -7,-4, -7,1/*mean (0.0233806), correlation (0.496568)*/,    -8,11, -7,-8/*mean (0.0236505), correlation (0.489719)*/,    -13,6, -12,-8/*mean (0.0268781), correlation (0.503487)*/,    2,4, 3,9/*mean (0.0323324), correlation (0.501938)*/,    10,-5, 12,3/*mean (0.0399235), correlation (0.494029)*/,    -6,-5, -6,7/*mean (0.0420153), correlation (0.486579)*/,    8,-3, 9,-8/*mean (0.0548021), correlation (0.484237)*/,    2,-12, 2,8/*mean (0.0616622), correlation (0.496642)*/,    -11,-2, -10,3/*mean (0.0627755), correlation (0.498563)*/,    -12,-13, -7,-9/*mean (0.0829622), correlation (0.495491)*/,    -11,0, -10,-5/*mean (0.0843342), correlation (0.487146)*/,    5,-3, 11,8/*mean (0.0929937), correlation (0.502315)*/,    -2,-13, -1,12/*mean (0.113327), correlation (0.48941)*/,    -1,-8, 0,9/*mean (0.132119), correlation (0.467268)*/,    -13,-11, -12,-5/*mean (0.136269), correlation (0.498771)*/,    -10,-2, -10,11/*mean (0.142173), correlation (0.498714)*/,    -3,9, -2,-13/*mean (0.144141), correlation (0.491973)*/,    2,-3, 3,2/*mean (0.14892), correlation (0.500782)*/,    -9,-13, -4,0/*mean (0.150371), correlation (0.498211)*/,    -4,6, -3,-10/*mean (0.152159), correlation (0.495547)*/,    -4,12, -2,-7/*mean (0.156152), correlation (0.496925)*/,    -6,-11, -4,9/*mean (0.15749), correlation (0.499222)*/,    6,-3, 6,11/*mean (0.159211), correlation (0.503821)*/,    -13,11, -5,5/*mean (0.162427), correlation (0.501907)*/,    11,11, 12,6/*mean (0.16652), correlation (0.497632)*/,    7,-5, 12,-2/*mean (0.169141), correlation (0.484474)*/,    -1,12, 0,7/*mean (0.169456), correlation (0.495339)*/,    -4,-8, -3,-2/*mean (0.171457), correlation (0.487251)*/,    -7,1, -6,7/*mean (0.175), correlation (0.500024)*/,    -13,-12, -8,-13/*mean (0.175866), correlation (0.497523)*/,    -7,-2, -6,-8/*mean (0.178273), correlation (0.501854)*/,    -8,5, -6,-9/*mean (0.181107), correlation (0.494888)*/,    -5,-1, -4,5/*mean (0.190227), correlation (0.482557)*/,    -13,7, -8,10/*mean (0.196739), correlation (0.496503)*/,    1,5, 5,-13/*mean (0.19973), correlation (0.499759)*/,    1,0, 10,-13/*mean (0.204465), correlation (0.49873)*/,    9,12, 10,-1/*mean (0.209334), correlation (0.49063)*/,    5,-8, 10,-9/*mean (0.211134), correlation (0.503011)*/,    -1,11, 1,-13/*mean (0.212), correlation (0.499414)*/,    -9,-3, -6,2/*mean (0.212168), correlation (0.480739)*/,    -1,-10, 1,12/*mean (0.212731), correlation (0.502523)*/,    -13,1, -8,-10/*mean (0.21327), correlation (0.489786)*/,    8,-11, 10,-6/*mean (0.214159), correlation (0.488246)*/,    2,-13, 3,-6/*mean (0.216993), correlation (0.50287)*/,    7,-13, 12,-9/*mean (0.223639), correlation (0.470502)*/,    -10,-10, -5,-7/*mean (0.224089), correlation (0.500852)*/,    -10,-8, -8,-13/*mean (0.228666), correlation (0.502629)*/,    4,-6, 8,5/*mean (0.22906), correlation (0.498305)*/,    3,12, 8,-13/*mean (0.233378), correlation (0.503825)*/,    -4,2, -3,-3/*mean (0.234323), correlation (0.476692)*/,    5,-13, 10,-12/*mean (0.236392), correlation (0.475462)*/,    4,-13, 5,-1/*mean (0.236842), correlation (0.504132)*/,    -9,9, -4,3/*mean (0.236977), correlation (0.497739)*/,    0,3, 3,-9/*mean (0.24314), correlation (0.499398)*/,    -12,1, -6,1/*mean (0.243297), correlation (0.489447)*/,    3,2, 4,-8/*mean (0.00155196), correlation (0.553496)*/,    -10,-10, -10,9/*mean (0.00239541), correlation (0.54297)*/,    8,-13, 12,12/*mean (0.0034413), correlation (0.544361)*/,    -8,-12, -6,-5/*mean (0.003565), correlation (0.551225)*/,    2,2, 3,7/*mean (0.00835583), correlation (0.55285)*/,    10,6, 11,-8/*mean (0.00885065), correlation (0.540913)*/,    6,8, 8,-12/*mean (0.0101552), correlation (0.551085)*/,    -7,10, -6,5/*mean (0.0102227), correlation (0.533635)*/,    -3,-9, -3,9/*mean (0.0110211), correlation (0.543121)*/,    -1,-13, -1,5/*mean (0.0113473), correlation (0.550173)*/,    -3,-7, -3,4/*mean (0.0140913), correlation (0.554774)*/,    -8,-2, -8,3/*mean (0.017049), correlation (0.55461)*/,    4,2, 12,12/*mean (0.01778), correlation (0.546921)*/,    2,-5, 3,11/*mean (0.0224022), correlation (0.549667)*/,    6,-9, 11,-13/*mean (0.029161), correlation (0.546295)*/,    3,-1, 7,12/*mean (0.0303081), correlation (0.548599)*/,    11,-1, 12,4/*mean (0.0355151), correlation (0.523943)*/,    -3,0, -3,6/*mean (0.0417904), correlation (0.543395)*/,    4,-11, 4,12/*mean (0.0487292), correlation (0.542818)*/,    2,-4, 2,1/*mean (0.0575124), correlation (0.554888)*/,    -10,-6, -8,1/*mean (0.0594242), correlation (0.544026)*/,    -13,7, -11,1/*mean (0.0597391), correlation (0.550524)*/,    -13,12, -11,-13/*mean (0.0608974), correlation (0.55383)*/,    6,0, 11,-13/*mean (0.065126), correlation (0.552006)*/,    0,-1, 1,4/*mean (0.074224), correlation (0.546372)*/,    -13,3, -9,-2/*mean (0.0808592), correlation (0.554875)*/,    -9,8, -6,-3/*mean (0.0883378), correlation (0.551178)*/,    -13,-6, -8,-2/*mean (0.0901035), correlation (0.548446)*/,    5,-9, 8,10/*mean (0.0949843), correlation (0.554694)*/,    2,7, 3,-9/*mean (0.0994152), correlation (0.550979)*/,    -1,-6, -1,-1/*mean (0.10045), correlation (0.552714)*/,    9,5, 11,-2/*mean (0.100686), correlation (0.552594)*/,    11,-3, 12,-8/*mean (0.101091), correlation (0.532394)*/,    3,0, 3,5/*mean (0.101147), correlation (0.525576)*/,    -1,4, 0,10/*mean (0.105263), correlation (0.531498)*/,    3,-6, 4,5/*mean (0.110785), correlation (0.540491)*/,    -13,0, -10,5/*mean (0.112798), correlation (0.536582)*/,    5,8, 12,11/*mean (0.114181), correlation (0.555793)*/,    8,9, 9,-6/*mean (0.117431), correlation (0.553763)*/,    7,-4, 8,-12/*mean (0.118522), correlation (0.553452)*/,    -10,4, -10,9/*mean (0.12094), correlation (0.554785)*/,    7,3, 12,4/*mean (0.122582), correlation (0.555825)*/,    9,-7, 10,-2/*mean (0.124978), correlation (0.549846)*/,    7,0, 12,-2/*mean (0.127002), correlation (0.537452)*/,    -1,-6, 0,-11/*mean (0.127148), correlation (0.547401)*/