#功能描述：生成多尺度、多寬高比的anchors龟梦。  
#          尺度為：128,256,512; 寬高比為：1:2,1:1,2:1  

import numpy as np  #提供矩陣運(yùn)算功能的庫  

#生成anchors總函數(shù)：ratios為一個列表库糠，表示寬高比為：1:2,1:1,2:1  
#2**x表示:2^x，scales:[2^3 2^4 2^5],即:[8 16 32]  
def generate_anchors(base_size=16, ratios=[0.5, 1, 2],  
                     scales=2**np.arange(3, 6)):  
    """ 
    Generate anchor (reference) windows by enumerating aspect ratios X 
    scales wrt a reference (0, 0, 15, 15) window. 
    """  
    base_anchor = np.array([1, 1, base_size, base_size]) - 1  #新建一個數(shù)組：base_anchor:[0 0 15 15]  
    ratio_anchors = _ratio_enum(base_anchor, ratios)  #枚舉各種寬高比  
    anchors = np.vstack([_scale_enum(ratio_anchors[i, :], scales)  #枚舉各種尺度，vstack:豎向合并數(shù)組  
                         for i in xrange(ratio_anchors.shape[0])]) #shape[0]:讀取矩陣第一維長度擂仍，其值為3  
    return anchors  

#用于返回width,height,(x,y)中心坐標(biāo)(對于一個anchor窗口)  
def _whctrs(anchor):  
    """ 
    Return width, height, x center, and y center for an anchor (window). 
    """  
    #anchor:存儲了窗口左上角戴尸，右下角的坐標(biāo)  
    w = anchor[2] - anchor[0] + 1  
    h = anchor[3] - anchor[1] + 1  
    x_ctr = anchor[0] + 0.5 * (w - 1)  #anchor中心點(diǎn)坐標(biāo)  
    y_ctr = anchor[1] + 0.5 * (h - 1)  
    return w, h, x_ctr, y_ctr  

#給定一組寬高向量，輸出各個anchor琅捏，即預(yù)測窗口生百，**輸出anchor的面積相等，只是寬高比不同**  
def _mkanchors(ws, hs, x_ctr, y_ctr):  
    #ws:[23 16 11]柄延，hs:[12 16 22],ws和hs一一對應(yīng)蚀浆。  
    """ 
    Given a vector of widths (ws) and heights (hs) around a center 
    (x_ctr, y_ctr), output a set of anchors (windows). 
    """  
    ws = ws[:, np.newaxis]  #newaxis:將數(shù)組轉(zhuǎn)置  
    hs = hs[:, np.newaxis]  
    #hstack、vstack:合并數(shù)組搜吧，生成三個anchors市俊，寬高比分別為2:1, 1:1, 1:2
    anchors = np.hstack((x_ctr - 0.5 * (ws - 1),      
                         y_ctr - 0.5 * (hs - 1),    #anchor：[[-3.5 2 18.5 13]  
                         x_ctr + 0.5 * (ws - 1),     #        [0  0  15  15]  
                         y_ctr + 0.5 * (hs - 1)))     #       [2.5 -3 12.5 18]]  
    return anchors  

#枚舉一個anchor的各種寬高比，anchor[0 0 15 15],ratios[0.5,1,2]  
def _ratio_enum(anchor, ratios):  
    """   列舉關(guān)于一個anchor的三種寬高比 1:2,1:1,2:1 
    Enumerate a set of anchors for each aspect ratio wrt an anchor. 
    """  

    w, h, x_ctr, y_ctr = _whctrs(anchor)  #返回寬高和中心坐標(biāo)滤奈，w:16,h:16,x_ctr:7.5,y_ctr:7.5  
    size = w * h   #size:16*16=256  
    size_ratios = size / ratios  #256/ratios[0.5,1,2]=[512,256,128]  
    #round()方法返回x的四舍五入的數(shù)字摆昧，sqrt()方法返回數(shù)字x的平方根  
    ws = np.round(np.sqrt(size_ratios)) #ws:[23 16 11]  
    hs = np.round(ws * ratios)    #hs:[12 16 22],ws和hs一一對應(yīng)。as:23&12  
    anchors = _mkanchors(ws, hs, x_ctr, y_ctr)  #給定一組寬高向量蜒程，輸出各個預(yù)測窗口  
    return anchors  

#枚舉一個anchor的各種尺度蜂怎，以anchor[0 0 15 15]為例,scales[8 16 32]  
def _scale_enum(anchor, scales):  
    """   列舉關(guān)于一個anchor的三種尺度 128*128,256*256,512*512 
    Enumerate a set of anchors for each scale wrt an anchor. 
    """  
    w, h, x_ctr, y_ctr = _whctrs(anchor) #返回寬高和中心坐標(biāo)，w:16,h:16,x_ctr:7.5,y_ctr:7.5  
    ws = w * scales   #[128 256 512]  
    hs = h * scales   #[128 256 512]  
    anchors = _mkanchors(ws, hs, x_ctr, y_ctr) #[[-56 -56 71 71] [-120 -120 135 135] [-248 -248 263 263]]  
    return anchors  

if __name__ == '__main__':  #主函數(shù)  
    import time  
    t = time.time()  
    a = generate_anchors()  #生成anchor（窗口）  
    print time.time() - t   #顯示時間  
    print a  
    from IPython import embed; embed()  

References

• https://github.com/rbgirshick/py-faster-rcnn/blob/master/lib/rpn/generate_anchors.py

• https://blog.csdn.net/xzzppp/article/details/52317863