algorithm - 在 numpy 中加速矢量化眼动追踪算法

Question

我正在尝试实现 Fabian Timm 的眼动追踪算法 [ http://www.inb.uni-luebeck.de/publikationen/pdfs/TiBa11b.pdf] (在此处找到:[ http://thume.ca/projects/2012/11/04/simple-accurate-eye-center-tracking-in-opencv/] )在 numpy 和 OpenCV 中，我遇到了麻烦。我认为我已经足够体面地矢量化了我的实现，但它仍然不够快，无法实时运行，而且它无法像我希望的那样准确地检测瞳孔。这是我第一次使用 numpy，所以我不确定我做错了什么。

def find_pupil(eye):
    eye_len = np.arange(eye.shape[0])
    xx,yy = np.meshgrid(eye_len,eye_len) #coordinates
    XX,YY = np.meshgrid(xx.ravel(),yy.ravel()) #all distance vectors
    Dx,Dy = [YY-XX, YY-XX] #y2-y1, x2-x1 -- simpler this way because YY = XXT
    Dlen = np.sqrt(Dx**2+Dy**2)
    Dx,Dy = [Dx/Dlen, Dy/Dlen] #normalized

    Gx,Gy = np.gradient(eye)
    Gmagn = np.sqrt(Gx**2+Gy**2)

    Gx,Gy = [Gx/Gmagn,Gy/Gmagn] #normalized
    GX,GY = np.meshgrid(Gx.ravel(),Gy.ravel())

    X = (GX*Dx+GY*Dy)**2
    eye = cv2.bitwise_not(cv2.GaussianBlur(eye,(5,5),0.005*eye.shape[1])) #inverting and blurring eye for use as w
    eyem = np.repeat(eye.ravel()[np.newaxis,:],eye.size,0)
    C = (np.nansum(eyem*X, axis=0)/eye.size).reshape(eye.shape)

    return np.unravel_index(C.argmax(), C.shape)

和其余代码:

def find_eyes(face):
    left_x, left_y = [int(floor(0.5 * face.shape[0])), int(floor(0.2 * face.shape[1]))]
    right_x, right_y = [int(floor(0.1 * face.shape[0])), int(floor(0.2 * face.shape[1]))]
    area = int(floor(0.2 * face.shape[0]))
    left_eye = (left_x, left_y, area, area)
    right_eye = (right_x, right_y, area, area)

    return [left_eye,right_eye]



faceCascade = cv2.CascadeClassifier("haarcascade_frontalface_default.xml")
video_capture = cv2.VideoCapture(0)

while True:
    # Capture frame-by-frame
    ret, frame = video_capture.read()

    gray = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)

    faces = faceCascade.detectMultiScale(
        gray,
        scaleFactor=1.1,
        minNeighbors=5,
        minSize=(30, 30),
        flags=cv2.CASCADE_SCALE_IMAGE
    )

    # Draw a rectangle around the faces
    for (x, y, w, h) in faces:
        cv2.rectangle(frame, (x, y), (x+w, y+h), (0, 255, 0), 2)
        roi_gray = gray[y:y+h, x:x+w]
        roi_color = frame[y:y+h, x:x+w]
        eyes = find_eyes(roi_gray)
        for (ex,ey,ew,eh) in eyes:
            eye_gray = roi_gray[ey:ey+eh,ex:ex+ew]
            eye_color = roi_color[ey:ey+eh,ex:ex+ew]
            cv2.rectangle(roi_color,(ex,ey),(ex+ew,ey+eh),(255,0,0),2)
            px,py = find_pupil(eye_gray)
            cv2.rectangle(eye_color,(px,py),(px+1,py+1),(255,0,0),2)

    # Display the resulting frame
    cv2.imshow('Video', frame)

    if cv2.waitKey(1) & 0xFF == ord('q'):
        break

# When everything is done, release the capture
video_capture.release()
cv2.destroyAllWindows()

Answer 1

您可以执行许多保存复制元素的操作，然后通过在创建允许 NumPy broadcasting 的单例维度后直接执行数学运算来执行一些数学运算。 .因此，会有两个好处 - 节省工作空间内存和性能提升的即时操作。此外，最后，我们可以用简化版本替换 nansum 计算。因此，考虑到所有这些理念，这里有一种改进的方法 -

def find_pupil_v2(face, x, y, w, h):    
    eye = face[x:x+w,y:y+h]
    eye_len = np.arange(eye.shape[0])

    N = eye_len.size**2
    eye_len_diff = eye_len[:,None] - eye_len
    Dlen = np.sqrt(2*((eye_len_diff)**2))
    Dxy0 = eye_len_diff/Dlen 

    Gx0,Gy0 = np.gradient(eye)
    Gmagn = np.sqrt(Gx0**2+Gy0**2)
    Gx,Gy = [Gx0/Gmagn,Gy0/Gmagn] #normalized

    B0 = Gy[:,:,None]*Dxy0[:,None,:]
    C0 = Gx[:,None,:]*Dxy0
    X = ((C0.transpose(1,0,2)[:,None,:,:]+B0[:,:,None,:]).reshape(N,N))**2

    eye1 = cv2.bitwise_not(cv2.GaussianBlur(eye,(5,5),0.005*eye.shape[1]))
    C = (np.nansum(X,0)*eye1.ravel()/eye1.size).reshape(eye1.shape)

    return np.unravel_index(C.argmax(), C.shape)

在 Dxy 处还剩下一个 repeat。可能可以避免该步骤，并且可以将 Dxy0 直接输入到使用 Dxy 给我们 X 的步骤中，但我没有没成功。 一切都转换为基于广播!

运行时测试和输出验证-

In [539]: # Inputs with random elements
     ...: face = np.random.randint(0,10,(256,256)).astype('uint8')
     ...: x = 40
     ...: y = 60
     ...: w = 64
     ...: h = 64
     ...: 

In [540]: find_pupil(face,x,y,w,h)
Out[540]: (32, 63)

In [541]: find_pupil_v2(face,x,y,w,h)
Out[541]: (32, 63)

In [542]: %timeit find_pupil(face,x,y,w,h)
1 loops, best of 3: 4.15 s per loop

In [543]: %timeit find_pupil_v2(face,x,y,w,h)
1 loops, best of 3: 529 ms per loop

看来我们正在接近 8x 加速!