Synergistic face detection and pose estimation with energy-based models
A method for human face detection that detects faces independently of their particular poses and simultaneously estimates those poses. Our method exhibits an immunity to variations in skin color, eyeglasses, facial hair, lighting, scale and facial expressions, and others. In operation, we train a convolutional neural network to map face images to points on a face manifold, and non-face images to points far away from that manifold, wherein that manifold is parameterized by facial pose. Conceptually, we view a pose parameter as a latent variable, which may be inferred through an energy-minimization process. To train systems based upon our inventive method, we derive a new type of discriminative loss function that is tailored to such detection tasks. Our method enables a multi-view detector that can detect faces in a variety of poses, for example, looking left or right (yaw axis), up or down (pitch axis), or tilting left or right (roll axis). Systems employing our method are highly-reliable, run at near real time (5 frames per second on conventional hardware), and is robust against variations in yaw (±90°), roll(±45°), and pitch(±60°).
1. A computer-implemented method of face detection and pose estimation, the method comprising the following steps: training a convolutional neural network to map facial images to points on a face manifold, parameterized by facial pose, and to map non-facial images to points away from the face manifold; and simultaneously determining, whether an image is a face from its proximity to the face manifold and an estimate of facial pose of that image from its projection to the face manifold;
wherein the training step further comprises the step(s) of: optimizing a loss function of three variables, wherein said variables include image, pose, and face/non-face characteristics of an image;
wherein the loss function is represented by:
Loss
(
W
)
=
1
S
1
∑
i
εS
1
L
1
(
W
,
Z
i
,
X
i
)
+
1
S
0
∑
i
εS
1
L
0
(
W
,
X
i
)
;
where S 1 is the set of training faces, S 0 is the set of non-faces, L 3 (W,Z 1 ,X 1 ) and L 0 (W,X 1 ) are loss functions for a face sample (with a known pose) and non-face sample, respectively.
2. The method of claim 1 , wherein said determination step comprises the step(s) of:
clamping X to an observed value (the image), and finding the values of Z and Y that minimize an energy function E W (Y,Z,X) according to the following relationship:
( Y , Z )= arg min Yε{Y},Zε{Z} E W ( Y,Z,X )
where {Y}={0, 1} and {Z}=[−90, 90]×[−45, 45] for yaw and roll variables.
3. The method of claim 2 , wherein the energy function for a face E W (1,Z,X), is the distance between the point produced by the network G W (X) and the point with pose Z on the manifold F(Z) according to the following relationship:
E W (1 ,Z,X )=∥ G W ( X )− F ( Z )∥.
4. The method of claim 3 wherein the energy function for a non-face E W (0,Z,X), is equal to a threshold constant T, independent of Z and X that may be represented by the following relationship:
E W ( Y,Z,X )= Y∥G W ( X )− F ( Z )∥+(1 −Y ) T.
5. The method of claim 1 wherein the determination step comprises:
finding an output label and pose having the smallest energy according to the following relationship:
Z =arg min Zε{Z} ∥G W ( X )− F ( Z )∥+)1 −Y ) T;
comparing this minimum distance, ∥G W (X)−F( Z )∥, to threshold T;
classifying X as a face if the minimum distance is smaller than T, otherwise classifying X as a non-face.