Contents

# Two-Dimensional Spatial Pyramid Pooling Forward Layer

The forward two-dimensional (2D) spatial pyramid pooling layer with pyramid height
L
N
is a form of non-linear downsampling of an input tensor
X
. The library supports four-dimensional input tensors
X
R
n
1
x
n
2
x
n
3
x
n
4
. 2D spatial pyramid pooling partitions the input tensor data into (2
l
)
2
subtensors/bins,
l
∈ {0, ...,
L
-1}, along dimensions
k
1
and
k
2
and computes the result in each subtensor. The computation is done according to the selected pooling strategy: maximum, average, or stochastic. The spatial pyramid pooling layer applies the pooling
L
times with different kernel sizes, strides, and paddings.

## Problem Statement

The library provides several spatial pyramid pooling layers:
• Spatial pyramid maximum pooling
• Spatial pyramid average pooling
• Spatial pyramid stochastic pooling
The following description applies to each of these layers.
Let
X
R
n
1
x
n
2
x
n
3
x
n
4
be the tensor of input data and
k
1
and
k
2
be the dimensions along which kernels are applied. Without loss of generality
k
1
and
k
2
are the last dimensions of the tensor
X
. For each level
l
∈ {0, ...,
L
-1} and number of bins
b
= 2
l
, the layer applies 2D pooling with parameters:
• Kernel sizes
• Strides
s
i
=
m
i
In the layout flattened along the dimension
n'
, the layer result is represented as a two-dimensional tensor
Y
R
n
1
x
n'
, where
.
The following figure illustrates the behavior of the spatial pyramid maximum pooling forward layer with pyramid height
L
= 2:

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Notice revision #20110804