Face Detection: Neural-Network-Based

Motivation

• Idea: Use a search-window to scan over an image
• Train a classifier to decide whether the search windows contains a face or not?

Detection

Simple neuron model

Topologies

Parameters

Adjustable Parameters are

• Connection weights (to be learned)

• Activation function (fixed)

• Number of layers (fixed)

• Number of neurons per layer (fixed)

Training

Backpropagation with gradient descent

Neural Network Based Face Detection¹

• Idea: Use an artifical neural network to detect upright frontal faces

  • Network receives as input a 20x20 pixel region of an image

  • output ranges from -1 (no face present) to +1 (face present)

  • the neural network „face-filter“ is applied at every location in the image

  • to detect faces with different sizes, the input image is repeatedly scaled down

Network Topology

• 20x20 pixel input retina
• 4 types of receptive hidden fields
• One real-valued output

System Overview

Network Training

Training Set

• 1050 normalized face images

• 15 face images generated by rotating and scaling original face images

• 1000 randomly chosen non-face images

Preprocessing

• correct for different lighting conditions (overall brightness, shadows)
• rescale images to fixed size

Histogram equalization

• Defines a mapping of gray levels $p$ into gray levels $q$ such that the distribution of $q$ is close to being uniform

• Stretches contrast (expands the range of gray levels)

• Transforms different input images so that they have similar intensity distributions (thus reducing the effect of different illumination)

• Example

  

• Algorithm

  • The probability of an occurrence of a pixel of level $i$ in the image:

    $$ p\left(x\_{i}\right)=\frac{n\_{i}}{n}, \qquad i \in 0, \ldots, L-1 $$
    • $L$: number of gray levels
    • $n\_i$: number of occurences of gray level $i$

  • Define $c$ as the cumulative distribution function:

    $$ c(i)=\sum\_{j=0}^{i} p\left(x\_{j}\right) $$

  • Create a transformation of the form

    $$ y\_i = T(x\_i) = c(i), \qquad y\_i \in [0, 1] $$

    will produce a level $y$ for each level $x$ in the original image, such that the cumulative probability function of $y$ will be linearized across the value range.

    $$ y\_{i}^{\prime}=y\_{i} \cdot(\max -\min )+\min $$

Training Procedure

1. Randomly choose 1000 non-face images

2. Train network to produce 1 for faces, -1 for non-faces

3. Run network on images containing no faces. Collect subimages in which network incorrectly identifes a face (output > 0)

4. Select up to 250 of these „false positives“ at random and add them to the training set as negative examples

Neural Network Based Face Filter

• Output of ANN defines a filter for faces

• Search

  • Scan input image with search window, apply ANN to search window

  • Input image needs to be rescaled in order to detect faces with different size

• Output needs to be post-processed

  • Noise removal

  • Merging overlapping detections

• Speed up can be achieved

  • Increase step size

  • Make ANN more flexible to translation

  • Hierarchical, pyramidal search

Localization and Ground-Truth

• For localization, the test data is mostly annotated with ground-truth bounding boxes

• Comparing hypotheses to Ground-Truth

  • Overlap

    $$ O = \frac{\text{GT } \cap \text{ DET}}{\text{GT } \cup \text{ DET}} $$

    

    Also called Intersection over Union (IoU)

  • Often used as threshold: Overlap>50%