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Essentially, a pooling operation executes the aggregation of feature types, reducing the dimensionality of the feature space. In neurological terms, neurons aggregate and process bioelectrical signals of various bioelectricity rates from other neurons which is equivalent to pooling. The max pooling rate is to process the signal which has the highest bioelectricity rate, while the mean pooling gives the average of involved signals. Similarly, the pooling strategy in artificial neural networks is to compress features, accelerate the computation, allow translational invariance, and reduce the risk of overfitting. Pooling operations can be in many forms, such as max pooling, mean pooling, stochastic pooling, etc.

1 Max pooling: Select the maximum value within an image window as the value of the corresponding pixel/voxel.

2 Mean pooling: Calculate the average value of an image window as the value of the corresponding pixel/voxel.

3 Stochastic pooling: Stochastic pooling first computes the probabilities for each region (Zeiler and Fergus 2013). In a simple way, the probability for each pixel can be calculated by dividing the pixel value by the sum of the values in the pooling window. Then, it randomly selects one value within each pooling region according to the probability distribution. Among these values, the one with the largest probability will be selected, but it is not to say that the largest value must be selected.

Generally speaking, mean pooling often retains the overall characteristics of the data and protrudes the background information, max pooling can reveal the textural information, and stochastic pooling has the advantages of max pooling and partially avoids the excessive distortion caused by max pooling. Figure 3.14 illustrates these three pooling strategies.

Figure 3.14. Illustration of the three types of pooling strategies.