maxPooling3dLayer
3D max pooling layer
Description
A 3D max pooling layer performs downsampling by dividing threedimensional 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 3D 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 3D 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 2D 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
Description
sets optional properties using one or more namevalue arguments.layer
= maxPooling3dLayer(poolSize
,Name=Value
)
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.
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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 3D 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 isceil(inputSize/stride)
, whereinputSize
is the height, width, or depth of the input andstride
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 sizep
to all the edges of the input.Threeelement vector
[a b c]
of nonnegative integers — Add padding of sizea
to the top and bottom, padding of sizeb
to the left and right, and padding of sizec
to the front and back of the input.2by3 matrix
[t l f;b r k]
of nonnegative integers — Add padding of sizet
to the top,b
to the bottom,l
to the left,r
to the right,f
to the front, andk
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
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)  2by3 matrix of nonnegative integers
Size of padding to apply to input borders, specified as 2by3 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
namevalue 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 setsPaddingMode
to"manual"
.If you set the
Padding
argument to"same"
, then the software automatically setsPaddingMode
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 isceil(inputSize/stride)
, whereinputSize
is the height, width, or depth of the input andstride
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
NumInputs
— Number of inputs
1
(default)
This property is readonly.
Number of inputs to the layer, returned as 1
. This layer accepts a
single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is readonly.
Input names, returned as {'in'}
. This layer accepts a single input
only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is readonly.
Number of outputs from the layer, returned as 1
. This layer has a
single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is readonly.
Output names, returned as {'out'}
. This layer has a single output
only.
Data Types: cell
Examples
Create Max Pooling 3D Layer with Nonoverlapping Pooling Regions
Create a max pooling 3D 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: [2x3 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 = 6x1 Layer array with layers: 1 '' 3D Image Input 28x28x28x3 images with 'zerocenter' normalization 2 '' 3D Convolution 20 5x5x5 convolutions with stride [1 1 1] and padding [0 0 0; 0 0 0] 3 '' ReLU ReLU 4 '' 3D Max Pooling 2x2x2 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 3D Layer with Overlapping Pooling Regions
Create a max pooling 3D 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: [2x3 double]
This layer creates pooling regions of size 3by2by2 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
3D Max Pooling Layer
A 3D max pooling layer extends the functionality of a max pooling
layer to a third dimension, depth. A max pooling layer performs downsampling by dividing
the input into rectangular or cuboidal pooling regions, and computing the maximum of each
region. To learn more, see the 2D Max Pooling Layer section of the maxPooling2dLayer
reference page.
The dimensions that the layer pools over depends on the layer input:
For 3D 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 3D 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 2D 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 formats consist of one or
more of these characters:
"S"
— Spatial"C"
— Channel"B"
— Batch"T"
— Time"U"
— Unspecified
For example, you can describe 2D image data that is represented as a 4D 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 









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











Version History
Introduced in R2019a
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