# US 2019/0244104 A1 · Method for improving computations of correlation values between surface roughness and terrain parameters

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- Number: US 2019/0244104 A1
- Document ID: US20190244104A1
- Status: Published application
- Kind: A1
- Application number: 15/886,860
- Filed: 2018-02-02
- Published: 2019-08-08
- Earliest claimed: 2018-02-02
- Assignees: Macau University of Science and Technology
- Applicants: Macau University of Science and Technology
- Inventors: Zhanchuan Cai; Aiju Li
- Web page: https://patentgrep.com/patent/US20190244104A1

## CPC

- G06V 10/82: using neural networks
- G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)}
- G06F 18/2413: based on distances to training or reference patterns
- G06N 3/084: Backpropagation, e.g. using gradient descent
- G06N 20/00: Machine learning
- G06V 20/13: Satellite images
- B64G 99/00: Subject matter not provided for in other groups of this subclass
- G06F 17/156: {using a domain transform, e.g. Fourier transform, polynomial transform, number theoretic transform}
- G06N 3/048: Activation functions
- G06V: IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- B64G: COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR

## Abstract

One embodiment is a method that improves computations of correlation values between a surface roughness and terrain parameters of a terrain surface. The method includes applying the terrain parameters as an input of a Back Propagation Neural Network (BPNN) and the surface roughness as an output of the BPNN; implementing a nonlinear mapping from the input to the output of the BPNN; generating a weight matrix (ω1) and a weight matrix (ω2); and improving computations of the correlation values by calculating a correlation matrix by ω2×ω1, calculating a unit weight which is a sum of absolute values in the correlation matrix, and dividing each value in the correlation matrix by the unit weight.

## Claims

### Claim 1

A method executed by a computer system that improves computations of correlation values between a surface roughness and terrain parameters of a terrain surface, the method comprising:
applying, by the computer system, the terrain parameters as an input of a Back Propagation Neural Network (BPNN) and the surface roughness as an output of the BPNN, wherein the BPNN includes an input layer, a hidden layer and an output layer;
implementing, by the computer system, a nonlinear mapping from the input to the output of the BPNN;
generating, by the computer system, a weight matrix (ω1) between the input layer and the hidden layer and a weight matrix (ω2) between the hidden layer and the output layer; and
improving computations of the correlation values by:
calculating, by the computer system, a correlation matrix by ω2×ω1;
calculating, by the computer system, a unit weight which is a sum of absolute values in the correlation matrix; and
dividing, by the computer system, each value in the correlation matrix by the unit weight.

### Claim 2 (depends on 1)

The method of claim 1, wherein the terrain parameters are selected from a group consisting of slope, aspect, curvature, plane curvature, slope variability and aspect ratio of the terrain surface.

### Claim 3 (depends on 1)

The method of claim 1 further comprising:
normalizing the input and the output of the BPNN to be between −1 and 1.

### Claim 4 (depends on 1)

The method of claim 1 further comprising
calculating, by the computer system, an error (MSE) between an actual output (Q) and an expected output (Y) of the BPNN by:
MSE
=
Σ

(
Y
-
Q
)
2
m
’
⋆
n
wherein where n is the dimension of the output layer and m′ is a number of neurons of the output layer; and
training, by the computer system, the BPNN until the error reaches a pre-determined value by changing ω1 and ω2.

### Claim 5 (depends on 1)

The method of claim 1, wherein the nonlinear mapping includes function f(x):
ƒ(x)=purelin[ω2×tan sig(ω1×X,b1),b2]
wherein tan sig has a function expressed as:
ƒ(x,ω)=(1−e−ωx)/(1+e−ωx)
wherein purelin has a function expressed as:
ƒ(x,ω)=ωx
where X is a matrix of six input terrain vectors:
X
=
[
x
1
,
1
x
1
,
2
⋯
x
1
,
m
x
2
,
1
x
2
,
2
⋯
x
2
,
m
⋮
⋮
⋮
⋮
x
6
,
1
x
6
,
2
⋯
x
6
,
m
]
where b1 is a threshold matrix between the input layer and the hidden layer, b2 is a threshold matrix between the hidden layer and the output layer and m is the column of input layer matrix.

### Claim 6 (depends on 1)

The method of claim 1, wherein the surface roughness is expressed as f(x):
f

(
x
)
=
ω
2
×
ω
1
×
X
where
ω
1
=
[
ω
1
,
1
ω
1
,
2
⋯
ω
1
,
6
ω
2
,
1
ω
2
,
2
⋯
ω
2
,
6
⋮
⋮
⋮
⋮
ω
8
,
1
ω
8
,
2
⋯
ω
8
,
6
]
,
ω
2
=
[
ω
1
,
1
ω
1
,
2
ω
1
,
3
ω
1
,
4
ω
1
,
5
ω
1
,
6
ω
1
,
7
ω
1
,
8
]
,
X
=
[
x
1
,
1
x
1
,
2
⋯
x
1
,
m
x
2
,
1
x
2
,
2
⋯
x
2
,
m
⋮
⋮
⋮
⋮
x
6
,
1
x
6
,
2
⋯
x
6
,
m
]
and m is the column of input layer matrix.

### Claim 7 (depends on 1)

The method of claim 1, wherein an output of a jth neuron of the hidden layer is expressed as Hj, and a kth output of the BPNN is expressed as Qk:
H
j
=
f

(
∑
i
=
1
n

(
ω
ij
-
b
j
)
)
,
j
=
1
,
2
,
⋯

,
l


Q
k
=
f

(
∑
j
=
1
l

(
ω
jk
-
d
k
)
)
,
k
=
1
,
2
,
⋯

,
m
’
where f is an activation function, n, l, and m′ are the number of neurons of the input layer, the hidden layer and the output layer respectively, ωij is a weight matrix between the input layer and hidden layer, ωjk is a weight matrix between the hidden layer and output layer, b and d are threshold matrices of the input layer and hidden layer, and the hidden layer and the output layer, respectively.

### Claim 8 (depends on 1)

The method of claim 1 further comprising:
calculating, by the computer system, the surface roughness by computing a difference between generated digital elevation models and morphological closing and opening operators, wherein the morphological closing and opening operators are constructed by finding a highest point and a lowest point reached by a Structuring Element (SE) shape.

### Claim 9

A computer system that generates an improved correlation graph that shows correlations between a surface roughness and terrain parameters of a lunar surface, the computer system comprising:
a processor;
a display;
a non-transitory computer-readable medium having stored therein instructions that when executed cause the processor to:
apply the terrain parameters as an input of a Back Propagation Neural Network (BPNN) and the surface roughness as an output of the BPNN, wherein the BPNN includes an input layer, a hidden layer and an output layer;
implement a nonlinear mapping from the input to the output of the BPNN;
generate a weight matrix (ω1) between the input layer and the hidden layer and a weight matrix (ω2) between the hidden layer and the output layer;
compute correlation values by:
calculating a correlation matrix by ω2×ω1;
calculating a unit weight which is a sum of absolute values in the correlation matrix; and
dividing each value in the correlation matrix by the unit weight; and
generate the improved correlation graph on the display by plotting the correlation values against the terrain parameters.

### Claim 10 (depends on 9)

The system of claim 9, wherein the terrain parameters are selected from a group consisting of slope, aspect, curvature, plane curvature, slope variability and aspect ratio of the lunar surface.

### Claim 11 (depends on 9)

The system of claim 9, wherein the instructions when executed further cause the processor to
calculate an error (MSE) between an actual output (Q) and an expected output (Y) of the BPNN by:
MSE
=
Σ

(
Y
-
Q
)
2
m
’
⋆
n
wherein n is the dimension of the output layer and m′ is a number of neurons of the output layer; and
train the BPNN until the error reaches a pre-determined value by changing ω1 and ω2.

### Claim 12 (depends on 9)

The system of claim 9, wherein the nonlinear mapping includes function f(x):
ƒ(x)=purelin[ω2×tan sig(ω1×X,b1),b2]
wherein tan sig has a function expressed as:
ƒ(x,ω)=(1−e−ωx)/(1+e−ωx)
wherein purelin has a function expressed as:
ƒ(x,ω)=ωx
where X is a matrix of six input terrain vectors:
X
=
[
x
1
,
1
x
1
,
2
⋯
x
1
,
m
x
2
,
1
x
2
,
2
⋯
x
2
,
m
⋮
⋮
⋮
⋮
x
6
,
1
x
6
,
2
⋯
x
6
,
m
]
where b1 is a threshold matrix between the input layer and the hidden layer, b2 is a threshold matrix between the hidden layer and the output layer and m is the column of input layer matrix.

### Claim 13 (depends on 9)

The system of claim 9, wherein the surface roughness is expressed as f(x):
f

(
x
)
=
ω
2
×
ω
1
×
X
where
ω
1
=
[
ω
1
,
1
ω
1
,
2
⋯
ω
1
,
6
ω
2
,
1
ω
2
,
2
⋯
ω
2
,
6
⋮
⋮
⋮
⋮
ω
8
,
1
ω
8
,
2
⋯
ω
8
,
6
]
,
ω
2
=
[
ω
1
,
1
ω
1
,
2
ω
1
,
3
ω
1
,
4
ω
1
,
5
ω
1
,
6
ω
1
,
7
ω
1
,
8
]
,
X
=
[
x
1
,
1
x
1
,
2
⋯
x
1
,
m
x
2
,
1
x
2
,
2
⋯
x
2
,
m
⋮
⋮
⋮
⋮
x
6
,
1
x
6
,
2
⋯
x
6
,
m
]
and m is the column of input layer matrix.

### Claim 14

A method that generates an improved correlation graph that shows correlations between a surface roughness and terrain parameters of a lunar surface, the method comprising:
applying, by the computer system, the terrain parameters as an input of a Back Propagation Neural Network (BPNN) and the surface roughness as an output of the BPNN, wherein the BPNN includes an input layer, a hidden layer and an output layer;
implementing, by the computer system, a nonlinear mapping from the input to the output of the BPNN;
generating, by the computer system, a weight matrix (ω1) between the input layer and the hidden layer and a weight matrix (ω2) between the hidden layer and the output layer;
computing, by the computer system, correlation values by:
calculating a correlation matrix by ω2×ω1;
calculating a unit weight which is a sum of absolute values in the correlation matrix;
dividing each value in the correlation matrix by the unit weight; and
generating, by the computer system and on a display, the improved correlation graph by plotting the correlation values against the terrain parameters.

### Claim 15 (depends on 14)

The method of claim 14, wherein the terrain parameters are selected from a group consisting of slope, aspect, curvature, plane curvature, slope variability and aspect ratio of the lunar surface.

### Claim 16 (depends on 14)

The method of claim 14 further comprising:
normalizing the input and the output of the BPNN to be between −1 and 1.

### Claim 17 (depends on 14)

The method of claim 14 further comprising,
calculating, by the computer system, an error (MSE) between an actual output (Q) and an expected output (Y) of the BPNN by:
MSE
=
Σ

(
Y
-
Q
)
2
m
’
⋆
n
wherein n is the dimension of the output layer and m′ is a number of neurons of the output layer; and
training, by the computer system, the BPNN until the error reaches a pre-determined value by changing ω1 and ω2.

### Claim 18 (depends on 14)

The method of claim 14, wherein the nonlinear mapping includes function f(x):
ƒ(x)=purelin[ω2×tan sig(ω1×X,b1),b2]
wherein tan sig has a function expressed as:
ƒ(x,ω)=(1−e−ωx)/(1+e−ωx)
wherein purelin has a function expressed as:
ƒ(x,ω)=ωx
where X is a matrix of six input terrain vectors:
X
=
[
x
1
,
1
x
1
,
2
⋯
x
1
,
m
x
2
,
1
x
2
,
2
⋯
x
2
,
m
⋮
⋮
⋮
⋮
x
6
,
1
x
6
,
2
⋯
x
6
,
m
]
where b1 is a threshold matrix between the input layer and the hidden layer, b2 is a threshold matrix between the hidden layer and the output layer.

### Claim 19 (depends on 14)

The method of claim 14, wherein the surface roughness is expressed as f(x):
f

(
x
)
=
ω
2
×
ω
1
×
X
where
ω
1
=
[
ω
1
,
1
ω
1
,
2
⋯
ω
1
,
6
ω
2
,
1
ω
2
,
2
⋯
ω
2
,
6
⋮
⋮
⋮
⋮
ω
8
,
1
ω
8
,
2
⋯
ω
8
,
6
]
,
ω
2
=
[
ω
1
,
1
ω
1
,
2
ω
1
,
3
ω
1
,
4
ω
1
,
5
ω
1
,
6
ω
1
,
7
ω
1
,
8
]
,
X
=
[
x
1
,
1
x
1
,
2
⋯
x
1
,
m
x
2
,
1
x
2
,
2
⋯
x
2
,
m
⋮
⋮
⋮
⋮
x
6
,
1
x
6
,
2
⋯
x
6
,
m
]
and m is the column of input layer matrix.

### Claim 20 (depends on 14)

The method of claim 14 further comprising:
calculating, by the computer system, the surface roughness by computing a difference between generated digital elevation models and morphological closing and opening operators, wherein the morphological closing and opening operators are constructed by finding a highest point and a lowest point reached by a Structuring Element (SE) shape.