# US 10,872,398 B2 · Apparatus and method for removing haze from image using fuzzy membership function, and computer program for performing the method

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- Number: US 10,872,398 B2
- Document ID: US10872398B2
- Status: Granted
- Kind: B2
- Application number: 16/190,609
- Filed: 2018-11-14
- Published: 2019-05-16
- Granted: 2020-12-22
- Earliest claimed: 2017-11-14
- Assignees: Chung Ang University Industry Academic Cooperation Foundation
- Applicants: Chung Ang University Industry Academic Cooperation Foundation
- Inventors: Joon Ki Paik; Ha Sil Park; Jin Ho Park; Hee Gwang Kim
- Web page: https://patentgrep.com/patent/US10872398B2

## CPC

- G06T 5/70: Denoising; Smoothing
- G06T 2207/20016: Hierarchical, coarse-to-fine, multiscale or multiresolution image processing; Pyramid transform
- G06T 2207/20072: Graph-based image processing
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

The apparatus for removing haze from an image using a fuzzy membership function includes memory configured to store computer-readable instructions; and a processor configured to execute the instructions, wherein the processor calculates a hazy value and a transmission map using an input image including a hazy component and generates a restored image from which the hazy component has been removed using the hazy value and the transmission map, and wherein the processor selects a first area in the input image, calculates a fuzzy membership function of pixels of the input image with respect to the hazy value using brightness values of the pixels of the input image and brightness values of pixels of the first area, and calculates the transmission map using the brightness values of pixels of the first area and the fuzzy membership function.

## Claims

### Claim 1

An apparatus for performing an operation of removing haze included in an image, comprising:
memory configured to store computer-readable instructions; and
a processor configured to execute the instructions,
wherein the processor calculates a hazy value and a transmission map using an input image including a hazy component and generates a restored image from which the hazy component has been removed using the hazy value and the transmission map;
wherein the processor selects a first area in the input image, calculates a fuzzy membership function of pixels of the input image with respect to the hazy value using brightness values of the pixels of the input image and brightness values of pixels of the first area, and calculates the transmission map using the brightness values of pixels of the first area and the fuzzy membership function;
wherein a function value of the fuzzy membership function is determined using a brightness value A that is a minimum value of the brightness values of the pixels of the input image, a brightness value B that is a maximum value of the brightness values of the pixels of the input image, a brightness value C that is a minimum value of the brightness values of the first area, and a brightness value D that is a maximum value of the brightness values of the first area; and
wherein the processor calculates the transmission map using a fuzzy membership function for a R channel of the pixels of the input image, a fuzzy membership function for a G channel of the pixels of the input image, a fuzzy membership function for a B channel of the pixels of the input image, a mean value of the brightness value C and the brightness value D for the R channel, a mean value of the brightness value C and the brightness value D for the G channel, and a mean value of the brightness value C and the brightness value D for the B channel.

### Claim 2 (depends on 1)

The apparatus of claim 1, wherein the processor determines the function value for each of the pixels of the input image,
wherein when a brightness value of a pixel of the input image is less than the brightness value A or greater than the brightness value B, the fuzzy membership function has a function value of 0,
wherein when a brightness value of a pixel of the input image is greater than or equal to the brightness value C and less than or equal to the brightness value D, the fuzzy membership function has a function value of 1,
wherein when the brightness value of a pixel of the input image is greater than or equal to the brightness value A and less than the brightness value C, the fuzzy membership function has a function value of “1−(the brightness value C−the brightness value of the pixel of the input image)/(the brightness value C−the brightness value A)”, and
wherein when the brightness value of a pixel of the input image is greater than or equal to the brightness value D and less than the brightness value B, the fuzzy membership function has a function value of “1−(the brightness value of the pixel of the input image−the brightness value D)/(the brightness value B−the brightness value D)”.

### Claim 3 (depends on 2)

The apparatus of claim 2, wherein the fuzzy membership function, brightness values of the pixel of the input image, the brightness value A, the brightness value B, the brightness value C, and the brightness value D is calculated or determined for each of R, G, and B channels.

### Claim 4 (depends on 1)

The apparatus of claim 1, wherein the transmission map is expressed by the following equation:
T
=
1
-
ω
·
μ
g
R
×
mean
⁢
⁢
A
R
+
μ
g
G
×
mean
⁢
⁢
A
G
+
μ
g
B
×
mean
⁢
⁢
A
B
mean
⁢
⁢
A
R
+
mean
⁢
⁢
A
G
+
mean
⁢
⁢
A
B
where T is the transmission map, μgR is the fuzzy membership function value for the R channel, μgG is the fuzzy membership function value for the G channel, μgB is the fuzzy membership function value for the B channel, mean AR is the mean value of the brightness value C and the brightness value D of the R channel, mean AG is the mean value of the brightness value C and the brightness value D for the G channel, mean AB is the mean value of the brightness value C and the brightness value D for the B channel, and ω is a parameter to control the amount of haze removal.

### Claim 5 (depends on 1)

The apparatus of claim 1, wherein the first area is an area having the maximum mean brightness value in the input image.

### Claim 6 (depends on 1)

The apparatus of claim 1, wherein the processor refines the transmission map using L1-norm regularization technique and generates the restored image using the refined transmission map.

### Claim 7

A method for removing haze from an image, the method being performed by an apparatus including a processor, the method comprising the steps of:
calculating a hazy value and a transmission map using an input image including a hazy component; and
generating a restored image from which the hazy component has been removed using the hazy value and the transmission map,
wherein the step of calculating selects a first area in the input image, calculates a fuzzy membership function of pixels of the input image with respect to the hazy value using brightness values of the pixels of the input image and brightness values of pixels of the first area, and calculates the transmission map using the brightness values of pixels of the first area and the fuzzy membership function;
wherein a function value of the fuzzy membership function is determined using a brightness value A that is a minimum value of the brightness values of the pixels of the input image, a brightness value B that is a maximum value of the brightness values of the pixels of the input image, a brightness value C that is a minimum value of the brightness values of the first area, and a brightness value D that is a maximum value of the brightness values of the first area; and
wherein the transmission map is calculated using a fuzzy membership function for a R channel of the pixels of the input image, a fuzzy membership function for a G channel of the pixels of the input image, a fuzzy membership function for a B channel of the pixels of the input image, a mean value of the brightness value C and the brightness value D for the R channel, a mean value of the brightness value C and the brightness value D for the G channel, and a mean value of the brightness value C and the brightness value D for the B channel.

### Claim 8

A computer program product stored on a non-transitory computer-readable medium, comprising instructions for causing a computer to execute the steps of:
calculating a hazy value and a transmission map using an input image including a hazy component; and
generating a restored image from which the hazy component has been removed using the hazy value and the transmission map,
wherein the step of calculating selects a first area in the input image, calculates a fuzzy membership function of pixels of the input image with respect to the hazy value using brightness values of the pixels of the input image and brightness values of pixels of the first area, and calculates the transmission map using the brightness values of pixels of the first area and the fuzzy membership function;
wherein a function value of the fuzzy membership function is determined using a brightness value A that is a minimum value of the brightness values of the pixels of the input image, a brightness value B that is a maximum value of the brightness values of the pixels of the input image, a brightness value C that is a minimum value of the brightness values of the first area, and a brightness value D that is a maximum value of the brightness values of the first area; and
wherein the transmission map is calculated using a fuzzy membership function for a R channel of the pixels of the input image, a fuzzy membership function for a G channel of the pixels of the input image, a fuzzy membership function for a B channel of the pixels of the input image, a mean value of the brightness value C and the brightness value D for the R channel, a mean value of the brightness value C and the brightness value D for the G channel, and a mean value of the brightness value C and the brightness value D for the B channel.