after one is reversed and shifted on the other (7.26). Since the convolution integral is
a measure of overlapping rate between two functions, it also is an indicator of the
similarity rate of the patterns. In the signal processing, convolution of two-time
domain functions, f(t) and g(t), is defined as
f à g
ð
Þ t
ð Þ ¼
Z 1
À1
f τ
ð Þg t À τ
ð
Þdτ
ð7:26Þ
Deep convolutional networks have multiple convolution, pooling, and activation
layers. The amount of weights to be trained can be so high as up to millions of levels
in a deep learning process. Deep convolutional neural networks start the process by
convolutional decomposition and usually end by fully connected neural network
layers (Fig. 7.22) for the classification outputs. Convolution in deep learning is
similar to the cross-correlation in signal or image processing (Goodfellow et al.
2016).
A widely used CNN architecture example consisting of two convolutional and
pooling layers, a fully connected layer, and a logistic regression classifier is shown in
Fig. 7.22. It can be used to predict if a satellite image patch belongs to specific crop
type or not.
Two-dimensional (discrete) convolutions of the 2D data patterns represented by
matrix A and matrix B are calculated as A*B¼C where
C m, n
½
¼
X
u
X
v
A m þ u, n þ v
½
∙ B u, v
½
ð7:27Þ
Each element of C is calculated as the sum of the products of a single element of
A with a single element of B. Hence each element of C is computed from the sum of
the element-wise multiplication of A and B. This structure of convolution is efficiently processed on the digital signal processors (DSPs) since they can be
implemented in terms of MAC (multiply, add, and carry)-type instructions. On the
other hand, graphical processor units (GPU) support this type of operation in a
parallel architecture consisting of GPU cores. GPU cards have become critical
hardware for performance requirement in deep learning applications.
Fig. 7.22 CNN scheme for image classification
7 Data Fusion in Agricultural Information Systems
133
a measure of overlapping rate between two functions, it also is an indicator of the
similarity rate of the patterns. In the signal processing, convolution of two-time
domain functions, f(t) and g(t), is defined as
f à g
ð
Þ t
ð Þ ¼
Z 1
À1
f τ
ð Þg t À τ
ð
Þdτ
ð7:26Þ
Deep convolutional networks have multiple convolution, pooling, and activation
layers. The amount of weights to be trained can be so high as up to millions of levels
in a deep learning process. Deep convolutional neural networks start the process by
convolutional decomposition and usually end by fully connected neural network
layers (Fig. 7.22) for the classification outputs. Convolution in deep learning is
similar to the cross-correlation in signal or image processing (Goodfellow et al.
2016).
A widely used CNN architecture example consisting of two convolutional and
pooling layers, a fully connected layer, and a logistic regression classifier is shown in
Fig. 7.22. It can be used to predict if a satellite image patch belongs to specific crop
type or not.
Two-dimensional (discrete) convolutions of the 2D data patterns represented by
matrix A and matrix B are calculated as A*B¼C where
C m, n
½
¼
X
u
X
v
A m þ u, n þ v
½
∙ B u, v
½
ð7:27Þ
Each element of C is calculated as the sum of the products of a single element of
A with a single element of B. Hence each element of C is computed from the sum of
the element-wise multiplication of A and B. This structure of convolution is efficiently processed on the digital signal processors (DSPs) since they can be
implemented in terms of MAC (multiply, add, and carry)-type instructions. On the
other hand, graphical processor units (GPU) support this type of operation in a
parallel architecture consisting of GPU cores. GPU cards have become critical
hardware for performance requirement in deep learning applications.
Fig. 7.22 CNN scheme for image classification
7 Data Fusion in Agricultural Information Systems
133