maxPooling3dLayer

3-D max pooling layer

Description

A 3-D max pooling layer performs downsampling by dividing three-dimensional input into cuboidal pooling regions, then computing the maximum of each region.

The dimensions that the layer pools over depends on the layer input:

• For 3-D image input (data with five dimensions corresponding to pixels in three spatial dimensions, the channels, and the observations), the layer pools over the spatial dimensions.

• For 3-D image sequence input (data with six dimensions corresponding to the pixels in three spatial dimensions, the channels, the observations, and the time steps), the layer pools over the spatial dimensions.

• For 2-D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer pools over the spatial and time dimensions.

Creation

Syntax

layer = maxPooling3dLayer(poolSize)

layer = maxPooling3dLayer(poolSize,Name=Value)

Description

layer = maxPooling3dLayer(poolSize) creates a 3-D max pooling layer and sets the PoolSize property.

layer = maxPooling3dLayer(poolSize,Name=Value) sets optional properties using one or more name-value arguments.

Input Arguments

poolSize — Dimensions of pooling regions

vector of three positive integers | positive integer

Dimensions of the pooling regions, specified as a vector of three positive integers [h w d], where h is the height, w is the width, and d is the depth. When creating the layer, you can specify poolSize as a scalar to use the same value for all three dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions poolSize.

Example: [2 1 1] specifies pooling regions of height 2, width 1, and depth 1.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: maxPooling3dLayer(2,Stride=3) creates a 3-D max pooling layer with pool size [2 2 2] and stride [3 3 3].

Stride — Step size for traversing input

[1 1 1] (default) | vector of three positive integers | positive integer

Step size for traversing the input in three dimensions, specified as a vector [a b c] of three positive integers, where a is the vertical step size, b is the horizontal step size, and c is the step size along the depth direction. When creating the layer, you can specify Stride as a scalar to use the same value for step sizes in all three directions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 3 1] specifies a vertical step size of 2, a horizontal step size of 3, and a step size along the depth of 1.

Padding — Input edge padding

0 (default) | array of nonnegative integers | "same"

Input edge padding, specified as one of these values:

• "same" — Add padding of size calculated by the software at training or prediction time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height, width, or depth of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, to the left and right, and to the front and back, if possible. If the padding in a given dimension has an odd value, then the software adds the extra padding to the input as postpadding. In other words, the software adds extra vertical padding to the bottom, extra horizontal padding to the right, and extra depth padding to the back of the input.

• Nonnegative integer p — Add padding of size p to all the edges of the input.

• Three-element vector [a b c] of nonnegative integers — Add padding of size a to the top and bottom, padding of size b to the left and right, and padding of size c to the front and back of the input.

• 2-by-3 matrix [t l f;b r k] of nonnegative integers — Add padding of size t to the top, b to the bottom, l to the left, r to the right, f to the front, and k to the back of the input. In other words, the top row specifies the prepadding and the second row defines the postpadding in the three dimensions.

Example: Padding=1 adds one row of padding to the top and bottom, one column of padding to the left and right, and one plane of padding to the front and back of the input.

Example: Padding="same" adds padding so that the output has the same size as the input (if the stride equals 1).

Name — Layer name

"" (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to layers with the name "".

This argument sets the Name property.

Data Types: char | string

Properties

Max Pooling

PoolSize — Dimensions of pooling regions

vector of three positive integers

Dimensions of the pooling regions, specified as a vector of three positive integers [h w d], where h is the height, w is the width, and d is the depth. When creating the layer, you can specify PoolSize as a scalar to use the same value for all three dimensions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 1 1] specifies pooling regions of height 2, width 1, and depth 1.

Stride — Step size for traversing input

[1 1 1] (default) | vector of three positive integers

Step size for traversing the input in three dimensions, specified as a vector [a b c] of three positive integers, where a is the vertical step size, b is the horizontal step size, and c is the step size along the depth direction. When creating the layer, you can specify Stride as a scalar to use the same value for step sizes in all three directions.

If the stride dimensions Stride are less than the respective pooling dimensions, then the pooling regions overlap.

The padding dimensions PaddingSize must be less than the pooling region dimensions PoolSize.

Example: [2 3 1] specifies a vertical step size of 2, a horizontal step size of 3, and a step size along the depth of 1.

PaddingSize — Size of padding

[0 0 0;0 0 0] (default) | 2-by-3 matrix of nonnegative integers

Size of padding to apply to input borders, specified as 2-by-3 matrix [t l f;b r k] of nonnegative integers, where t and b are the padding applied to the top and bottom in the vertical direction, l and r are the padding applied to the left and right in the horizontal direction, and f and k are the padding applied to the front and back along the depth. In other words, the top row specifies the prepadding and the second row defines the postpadding in the three dimensions.

When you create a layer, use the Padding name-value argument to specify the padding size.

Example: [1 2 4; 1 2 4] adds one row of padding to the top and bottom, two columns of padding to the left and right, and four planes of padding to the front and back of the input.

PaddingMode — Method to determine padding size

"manual" (default) | "same"

Method to determine padding size, specified as "manual" or "same".

The software automatically sets the value of PaddingMode based on the Padding argument value you specify when creating a layer.

• If you set the Padding argument to a scalar or a vector of nonnegative integers, then the software automatically sets PaddingMode to "manual".

• If you set the Padding argument to "same", then the software automatically sets PaddingMode to "same" and calculates the size of the padding at training time so that the output has the same size as the input when the stride equals 1. If the stride is larger than 1, then the output size is ceil(inputSize/stride), where inputSize is the height, width, or depth of the input and stride is the stride in the corresponding dimension. The software adds the same amount of padding to the top and bottom, to the left and right, and to the front and back, if possible. If the padding in a given dimension has an odd value, then the software adds the extra padding to the input as postpadding. In other words, the software adds extra vertical padding to the bottom, extra horizontal padding to the right, and extra depth padding to the back of the input.

The MaxPooling3DLayer object stores this property as a character vector.

Layer

Name — Layer name

'' (default) | character vector | string scalar

Layer name, specified as a character vector or a string scalar. For Layer array input, the trainnet and dlnetwork functions automatically assign names to unnamed layers.

The MaxPooling3DLayer object stores this property as a character vector.

Data Types: char | string

NumInputs — Number of inputs

Read-only: 1 (default)

This property is read-only.

Number of inputs to the layer, stored as 1. This layer accepts a single input only.

Data Types: double

InputNames — Input names

Read-only: {'in'} (default)

This property is read-only.

Input names, stored as {'in'}. This layer accepts a single input only.

Data Types: cell

NumOutputs — Number of outputs

Read-only: 1 (default)

This property is read-only.

Number of outputs from the layer, stored as 1. This layer has a single output only.

Data Types: double

OutputNames — Output names

Read-only: {'out'} (default)

This property is read-only.

Output names, stored as {'out'}. This layer has a single output only.

Data Types: cell

Examples

Create Max Pooling 3-D Layer with Nonoverlapping Pooling Regions

Create a max pooling 3-D layer with nonoverlapping pooling regions.

layer = maxPooling3dLayer(2,Stride=2)

layer = 
  MaxPooling3DLayer with properties:

           Name: ''
     NumOutputs: 1
    OutputNames: {'out'}

   Hyperparameters
       PoolSize: [2 2 2]
         Stride: [2 2 2]
    PaddingMode: 'manual'
    PaddingSize: [2×3 double]

The height, width, and depth of the cuboidal regions (pool size) are 2. The step size for traversing the images (stride) is 2 in all dimensions. The pooling regions do not overlap because the stride is greater than or equal to the corresponding pool size in all dimensions.

Include a max pooling layer with nonoverlapping regions in a Layer array.

layers = [ ...
    image3dInputLayer([28 28 28 3])
    convolution3dLayer(5,20)
    reluLayer
    maxPooling3dLayer(2,Stride=2)
    fullyConnectedLayer(10)
    softmaxLayer]

layers = 
  6×1 Layer array with layers:

     1   ''   3-D Image Input   28×28×28×3 images with 'zerocenter' normalization
     2   ''   3-D Convolution   20 5×5×5 convolutions with stride [1  1  1] and padding [0  0  0; 0  0  0]
     3   ''   ReLU              ReLU
     4   ''   3-D Max Pooling   2×2×2 max pooling with stride [2  2  2] and padding [0  0  0; 0  0  0]
     5   ''   Fully Connected   10 fully connected layer
     6   ''   Softmax           softmax

Create Max Pooling 3-D Layer with Overlapping Pooling Regions

Create a max pooling 3-D layer with overlapping pooling regions and padding for the top and bottom of the input.

layer = maxPooling3dLayer([3 2 2],'Stride',2,'Padding',[1 0 0])

layer = 
  MaxPooling3DLayer with properties:

           Name: ''
     NumOutputs: 1
    OutputNames: {'out'}

   Hyperparameters
       PoolSize: [3 2 2]
         Stride: [2 2 2]
    PaddingMode: 'manual'
    PaddingSize: [2×3 double]

This layer creates pooling regions of size 3-by-2-by-2 and takes the maximum of the twelve elements in each region. The stride is 2 in all dimensions. The pooling regions overlap because there are stride dimensions Stride that are less than the respective pooling dimensions PoolSize.

Algorithms

3-D Max Pooling Layer

A 3-D max pooling layer extends the functionality of a max pooling layer to a third dimension, depth. A max pooling layer performs down-sampling by dividing the input into rectangular or cuboidal pooling regions, and computing the maximum of each region. To learn more, see the 2-D Max Pooling Layer section of the maxPooling2dLayer reference page.

The dimensions that the layer pools over depends on the layer input:

• For 3-D image input (data with five dimensions corresponding to pixels in three spatial dimensions, the channels, and the observations), the layer pools over the spatial dimensions.

• For 3-D image sequence input (data with six dimensions corresponding to the pixels in three spatial dimensions, the channels, the observations, and the time steps), the layer pools over the spatial dimensions.

• For 2-D image sequence input (data with five dimensions corresponding to the pixels in two spatial dimensions, the channels, the observations, and the time steps), the layer pools over the spatial and time dimensions.

Layer Input and Output Formats

Layers in a layer array or layer graph pass data to subsequent layers as formatted dlarray objects. The format of a dlarray object is a string of characters in which each character describes the corresponding dimension of the data. The format consists of one or more of these characters:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, you can describe 2-D image data that is represented as a 4-D array, where the first two dimensions correspond to the spatial dimensions of the images, the third dimension corresponds to the channels of the images, and the fourth dimension corresponds to the batch dimension, as having the format "SSCB" (spatial, spatial, channel, batch).

You can interact with these dlarray objects in automatic differentiation workflows, such as those for developing a custom layer, using a functionLayer object, or using the forward and predict functions with dlnetwork objects.

This table shows the supported input formats of MaxPooling3DLayer objects and the corresponding output format. If the software passes the output of the layer to a custom layer that does not inherit from the nnet.layer.Formattable class, or a FunctionLayer object with the Formattable property set to 0 (false), then the layer receives an unformatted dlarray object with dimensions ordered according to the formats in this table. The formats listed here are only a subset. The layer may support additional formats such as formats with additional "S" (spatial) or "U" (unspecified) dimensions.

Input Format	Output Format
"SSSCB" (spatial, spatial, spatial, channel, batch)	"SSSCB" (spatial, spatial, spatial, channel, batch)
"SSCBT" (spatial, spatial, channel, batch, time)	"SSCBT" (spatial, spatial, channel, batch, time)
"SSSCBT" (spatial, spatial, spatial, channel, batch, time)	"SSSCBT" (spatial, spatial, spatial, channel, batch, time)
"SSSB" (spatial, spatial, spatial, batch)	"SSSB" (spatial, spatial, spatial, batch)

In dlnetwork objects, MaxPooling3DLayer objects also support these input and output format combinations.

Input Format	Output Format
"SSSC" (spatial, spatial, spatial, channel)	"SSSC" (spatial, spatial, spatial, channel)
"SSCT" (spatial, spatial, channel, time)	"SSCT" (spatial, spatial, channel, time)
"SSSCT" (spatial, spatial, spatial, channel, time)	"SSSCT" (spatial, spatial, spatial, channel, time)
"SSBT" (spatial, spatial, batch, time)	"SSBT" (spatial, spatial, batch, time)
"SSSBT" (spatial, spatial, spatial, batch, time)	"SSSBT" (spatial, spatial, spatial, batch, time)

Version History

Introduced in R2019a