CN104778713B - A kind of image processing method - Google Patents

A kind of image processing method Download PDF

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CN104778713B
CN104778713B CN201510206329.8A CN201510206329A CN104778713B CN 104778713 B CN104778713 B CN 104778713B CN 201510206329 A CN201510206329 A CN 201510206329A CN 104778713 B CN104778713 B CN 104778713B
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straight line
image
intermediate image
road
obtains
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CN104778713A (en
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佘青云
卢宗庆
张文健
廖庆敏
仝武军
李丽
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Shenzhen Graduate School Tsinghua University
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Shenzhen Graduate School Tsinghua University
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Abstract

The invention discloses a kind of image processing method, including road vanishing Point Detection Method step, road vanishing Point Detection Method step comprises the following steps:Morphological Gradient treatment is carried out to image and obtains the first intermediate image;Binary conversion treatment is carried out to the first intermediate image and obtains the second intermediate image;Morphological scale-space is carried out to the second intermediate image and obtains the 3rd intermediate image;To every a line of the 3rd intermediate image:By pixel value carry out it is cumulative obtain row pixel value and, using row pixel value and maximum corresponding row as image Horizon line position;Rim detection is carried out to the parts of images in the first intermediate image below the position of horizon and obtains the 4th intermediate image;Straight-line detection is carried out to the 4th intermediate image and obtains the 5th intermediate image, obtain the straight line in the 5th intermediate image;Road end point is determined from intersection point.The present invention can realize good road Identification and Chinese herbaceous peony target detection.

Description

A kind of image processing method
【Technical field】
The present invention relates to image processing method field.
【Background technology】
With expanding economy, car ownership is greatly increased in recent years, and this brings immense pressure to traffic system.One The fairly perfect intelligent DAS (Driver Assistant System) of set, the incidence to reducing traffic accident will play very big effect.Present market Upper to be mainly what is realized by infrared radar and computer vision, the sharpest edges of infrared radar are can to obtain target Distance and scope, but cost is relatively high, and rate of false alarm is big;Method based on computer vision, low cost, volume It is small, it is easy to install and safeguard, and its image processing algorithm being based on has transplanting characteristic very well.
Some are based on the intelligent DAS (Driver Assistant System) of computer vision at present, and its Road Detection and Chinese herbaceous peony target detection are not It is perfect.
【The content of the invention】
In order to overcome the deficiencies in the prior art, the invention provides a kind of image processing method, with simplified process method and Improve treatment effect.
A kind of image processing method, including road vanishing Point Detection Method step, the road vanishing Point Detection Method step are included such as Lower step:
S1, Morphological Gradient treatment is carried out to image and obtains the first intermediate image;
S2, carries out binary conversion treatment and obtains the second intermediate image to first intermediate image;
S3, carries out Morphological scale-space and obtains the 3rd intermediate image to second intermediate image;
S4, to every a line of the 3rd intermediate image:By pixel value carry out it is cumulative obtain row pixel value and, by row pixel It is worth the Horizon line position as described image with maximum corresponding row;
S5, carries out rim detection and obtains to the parts of images in first intermediate image below the Horizon line position To the 4th intermediate image;
S6, straight-line detection is carried out to the 4th intermediate image and obtains the 5th intermediate image, obtains the 5th middle graph Straight line as in;
S7, the intersection point of straight line two-by-two in the straight line obtained in obtaining step S6 determines road end point from the intersection point.
In one embodiment,
Straight line in 5th intermediate image is handled as follows:
Slope screens step:Straight line of the selection slope within setting slope range;
Length screens step:Length according to straight line carries out sequence from long to short, and selection is setting straight before ranking Line.
In one embodiment,
In slope screening step, straight line of the absolute value of slope within [0.01,10] is selected;
After slope screens step and length screening step, also comprise the following steps:
By the absolute value of straight slope fall [i, i+1) in the range of straight line be included into in i-th straight line group:
H (i)=# i-1 < | K 'j|≤i, j=1,2 ..., N }, i=1,2 ..., 10;
Wherein, h (i) represents the number of the i-th straight line group cathetus, and N represents the total number of current screening straight line, K'jIt is jth The slope absolute value of bar straight line, # represent be how many bar straight slope fall (i-1, i] in;
Further according to the size of h (i), descending sort is carried out to h (i), obtain h (w) ', w=1,2 ..., 10:
Cumulative and H (r) is calculated again:
The straight line in suitable straight line group s is chosen again:
In one embodiment,
After suitable straight line group s is chosen, step S7 also comprises the following steps:
The straight line that will be obtained is numbered according to the size of slope, then straight line is divided according to the odd even of sequence number, very The straight line collection of several numbers is combined into Θodd, the straight line collection of even number is combined into Θeven, then ask for ΘoddIn any bar straight line and Θeven In the intersection point of any bar straight line be initial road end point, the initial of initial road end point is determined by following formula Divide the set v of v (x, y):
Wherein, PiAnd PjWhat is represented respectively is the abscissa and ordinate of intersection point,What is represented is floor operation, and # is represented Be that how many straight-line intersection falls at position (x, y) place, what m and n was represented respectively is the length and height of described image;
Final score V (x, y) of road end point is calculated by following formula:
Wherein Φ (i, j) is weighted factor, and what (i, j) was represented is coordinate points on image, and it is poor that σ represents Gauss standard, l generations Table is the mask size for weighting;
The corresponding pixels of V (x, y) of top score are chosen as final road end point.
In one embodiment,
Also include Road Detection step, the Road Detection step comprises the following steps:
To in first intermediate image be located at the Horizon line position below parts of images in texture than more consistent Part is divided into initial road region;
Convex closure treatment is carried out to the initial road region and obtains transition road area;
In the transition road area, similar pixel is polymerized to a super-pixel block;
For the super-pixel block of the transition road area adjacent edges, if in pixel in the super-pixel block, Belong to the number of transition road area more than certain proportion, then the super-pixel block is included into the transition road area, so that Obtain final road.
In one embodiment,
Also include Chinese herbaceous peony target detecting step, the Chinese herbaceous peony target detecting step comprises the following steps:
One group of pyramid of the image of N number of level is obtained according to described image;
The image to pyramidal N number of level of described image carries out Morphological Gradient treatment successively;
The image normalization of each level that will be processed by Morphological Gradient and is carried out to the original scale of described image Weighting is averaging and obtains initial conspicuousness score s'(x):
Wherein, G (Ik(x)) refer to yardstick k hypographs IkX () is after Morphological Gradient is processed and is stretched to original scale As a result;
To initial conspicuousness score s'(x) weighting of space and color is carried out, so as to obtain final conspicuousness score s (x0):
Wherein, x0What is represented is the position of point to be calculated, and that x is represented is x0R neighborhood positions, s'(x0) that represent is x0 The initial conspicuousness score at place, δ1And δ2Represent that Gauss standard is poor respectively;
According to conspicuousness score s (x0) Chinese herbaceous peony target is analyzed.
In one embodiment,
The Chinese herbaceous peony target detecting step also comprises the following steps:
The optical flow field of described image is obtained, Chinese herbaceous peony target is analyzed according to the optical flow field.
In one embodiment,
The Chinese herbaceous peony target detecting step also comprises the following steps:
Chinese herbaceous peony target is analyzed according to Plantaginales target final score O (x);
Wherein, ξ1With ξ2It is weight coefficient,It is s (x0) result after normalization,It is F (x0) after normalization Result, OF (x0) be described image x0According to the target detection score of optical flow field, vp is the coordinate of the road end point at place Position, d is the catercorner length of described image.
For road detecting section, the present invention is calculated without extremely complex algorithm, so disposed of in its entirety speed ratio is very fast, The color characteristics of road are independent of simultaneously, and generalization ability is stronger.
For Chinese herbaceous peony target detection part, and the present invention is utilized be target kinetic characteristic and target conspicuousness this Two characteristics for being not easy to be changed by environment, so in the case where there is target occlusion, still can well realize that target is examined Survey.
【Brief description of the drawings】
Fig. 1 is the schematic flow sheet of the image processing method of an embodiment of the present invention;
Fig. 2 is the expansive working schematic diagram of an embodiment of the present invention;
Fig. 3 is the etching operation schematic diagram of an embodiment of the present invention;
Fig. 4 is the convex closure treatment schematic diagram of an embodiment of the present invention.
【Specific embodiment】
The preferred embodiment invented is described in further detail below.
As shown in figure 1, a kind of image processing method of embodiment, including road vanishing Point Detection Method step, the road disappears Point detecting step is lost to comprise the following steps:
S1, Morphological Gradient treatment is carried out to the image that vehicle front camera is obtained and obtains the first intermediate image.
What road vanishing Point Detection Method was mainly utilized is that the smoothness properties of sky realizes detection with the architectural characteristic of road.For Influence of the noise to result is reduced, in most the starting of road vanishing Point Detection Method, smoothness properties of the present invention based on sky, to figure As carrying out Morphological Gradient treatment:
Wherein, molecules present be image initial Morphological Gradient, IdilaWhat x () represented is to carry out expansion to image Result figure afterwards, IeroWhat x () represented is the result figure after corroding to image.In order to reduce uneven illumination and weak side Influence of the edge to result, Morphological Gradient has been carried out herein local normalized (be in denominator to each pixel, Initial configuration gradient is normalized using value larger in the spot corrosion and expansion).Herein, why shape is used State gradient is processed, because Morphological Gradient has good inhibiting effect to weak edge, thus can be well Suppress the influence of the noises such as cloud, shade.
Expansion is exactly the operation for seeking local maximum, core B and figure I convolution, that is, calculate the pixel in the region of core B coverings Maximum, and this maximum is assigned to the pixel that reference point is specified.Highlight regions in image can thus be made gradually Increase.Its mathematic(al) representation is shown in shown in formula (2):
What wherein x was represented is certain pixel on image, and what x ' was represented is in the neighborhood centered on pixel x Coordinate points, what I (x) was represented is the pixel value of pixel x on original image, and element (x ') represents in the region of core B coverings Interior pixel x '.
As shown in Fig. 2 what A represented is original image, what B was represented is core for the schematic diagram of expansion.
Corrosion is exactly the operation for seeking local minimum, is the reverse operating of expansion, shown in its mathematics formula such as formula (3):
Its schematic diagram is as shown in Figure 3.
S2, carries out binary conversion treatment and obtains the second intermediate image to first intermediate image.
In one embodiment, otsu threshold process, threshold value can be used to use 1.3 times of otsu threshold values.
S3, carries out Morphological scale-space and obtains the 3rd intermediate image to second intermediate image.Morphological scale-space can be wrapped Expansion and corrosion treatment are included, for example, repeatedly at expansion process and a corrosion treatment, or multiple expansion process and multiple corrosion Reason etc..
S4, to every a line of the 3rd intermediate image:By pixel value carry out it is cumulative obtain row pixel value and, by row pixel It is worth the Horizon line position as described image with maximum corresponding row.
S5, carries out rim detection and obtains to the parts of images in first intermediate image below the Horizon line position To the 4th intermediate image.
Because most of road may not include strong edge, so in the present embodiment, before straight-line detection is carried out first The mode detected using gradient realizes that edge strengthens, and the first intermediate image has already been through Morphological Gradient treatment.Based on road The architectural characteristic on road, canny edge findings are carried out to the image below horizon, and processing mode is shown in shown in formula (4):
Wherein, what R was represented is horizon lower zone, and I (x) represents the pixel value at the x of position on original image, and W is represented Canny edge detection operators, TlowAnd ThighWhat is represented is the high-low threshold value of canny operators, and what δ was represented is Gaussian filter Variance,What is represented is convolution symbol.
S6, straight-line detection is carried out to the 4th intermediate image and obtains the 5th intermediate image, obtains the 5th middle graph Straight line as in.
It is contemplated that bend and road such as block at the appearance of phenomenon, so straight-line detection can be examined using lsd straight lines Survey.Afterwards further according to straight line various characteristics (straight length, straight slope, the statistical property of straight slope) to obtain straight line Screened.In the present embodiment, straight line screening is divided into three steps altogether:
Slope based on straight line carries out straight line screening:
In real scene, most horizontal and vertical straight line is from house, trees, vehicle etc., so being Obtain to the significant straight line of road vanishing Point Detection Method, the present embodiment only considers slope absolute value size in [0.01,10] model Enclose interior straight line.
Length based on straight line carries out straight line screening:
Because lsd is a kind of local Straight Line Extraction, so the straight line that detection is obtained there will necessarily be many noise spots, And straight length is shorter, the possibility that it belongs to noise is bigger, so in the present embodiment, eliminating length less than certain threshold value Straight line.Due to current embodiment require that adapt to different driving environments, so the threshold value chosen here is self adaptation:Based on straight line Length (from long to short) is ranked up to straight line, then only retain wherein preceding 90% straight line.
Statistical property based on straight slope is screened:
The straight line obtained by the screening of above-mentioned two step is obtained, the absolute value of straight slope is obtained, due to by above-mentioned two After step, the slope absolute value of straight line is within [0.01,10], so at this moment being quantified the slope of straight line, rule is:Fall [i, i+1) in the range of straight line mark be included into in i-th straight line group, shown in formula is expressed as follows:
H (i)=# i-1 < | K 'j|≤i, j=1,2 ..., N }, i=1,2 ..., 10 (5)
Wherein, N represents the total number of current screening straight line, | K 'j| it is the absolute value of straight line j slopes, what " # " was represented is have A how many straight slope fall (i-1, i] in.
Then further according to the size of h (i), descending sort is carried out to h (i), obtains h (w) ', w=1,2 ..., 10, i.e.,:
H (1) ' > h (2) ' > ... h (10) ', by formula 6 add up again afterwards obtains cumulative and H (r):
Then the straight line in suitable s is chosen according still further to formula 7:
So far, straight line screening is fully completed.
, it is necessary to tentatively be given a mark to straight line after straight line needed for obtaining, to obtain initial road end point.Specific side Case is:The straight line that obtains will be screened and be numbered (1,2,3 ..., N ') according to slope size from small to large, then by straight line according to it The odd even of sequence number is divided, and the straight line aggregated label of odd number is Θodd, the straight line aggregated label of even number is Θeven, so After ask for ΘoddAny bar straight line and ΘevenThe intersection point of middle any bar straight line, should be initial road end point, by such as following formula Sub (8) determine the set v of the initial score v (x, y) of initial road end point, the i.e. initial shot chart of road end point:
Wherein, PiAnd PjWhat is represented respectively is horizontal stroke, the ordinate of intersection point,What is represented is floor operation, and what " # " was represented is How many straight-line intersection falls at position (x, y) place, and what m and n was represented respectively is the length and height of image.
Because also there is noise jamming in the initial road end point for obtaining, and in the presence of certain error, it is necessary to add sky Between information it is further corrected, so in the present embodiment, add spatial information, the method pair weighted using Gauss The initial shot chart picture of road end point carries out further weighting marking, obtains the final score figure of road end point, specifically It is shown below:
Wherein, Φ (i, j) is weighted factor, and what (i, j) was represented is the coordinate points on image, and it is poor that σ represents Gauss standard, Value in embodiment is fixed, is 100, and formula (10) is that image is weighted, and what l was represented is the mask size of weighting, Integer.
Finally, the corresponding pixels of V (x, y) of top score are chosen as final road end point (x0,y0)。
A kind of image processing method of embodiment, also including Road Detection step, the Road Detection step includes as follows Step:
To in first intermediate image be located at the Horizon line position below parts of images in texture than more consistent Part is divided into initial road region;
Convex closure treatment is carried out to the initial road region and obtains transition road area;Convex closure similar to an elastic threads, All of point is all covered in elastic threads, its schematic diagram is as shown in Figure 4.Due to the road area edge that at this moment obtains also very It is coarse, so needing to be further processed road edge.
In the transition road area, similar pixel is polymerized to a super-pixel block;
For the super-pixel block of the transition road area adjacent edges, if in pixel in the super-pixel block, Belong to the number of transition road area more than certain proportion, then the super-pixel block is included into the transition road area, so that Obtain final road.
A kind of image processing method of embodiment, also including Chinese herbaceous peony target detecting step, the Chinese herbaceous peony target detecting step Comprise the following steps:
The optical flow field of described image is obtained, Chinese herbaceous peony target is analyzed according to the optical flow field.Optical flow field refers to image The apparent motion of grayscale mode, it is a two-dimensional vector field, and the information that it is included is the transient motion speed arrow of each picture point Amount information.The purpose for studying optical flow field is exactly the sports ground being not directly available for the approximate calculation from sequence image.Light stream What is portrayed is the sports ground of target, and the score of light stream detection is higher, shows that corresponding region is got over and there may exist obstacle target.
Be analyzed by operation to image, it is possible to achieve target detection, but due to target velocity magnitude just Than the distance that road end point is arrived in it, it is possible to find out it is nearer apart from road end point, its speed just it is smaller, so at a distance Target speed in light stream be difficult embody, at this moment need another mode to process image, to obtain Far field target.Because target is for road, its conspicuousness is stronger.So Objective extraction can be carried out using conspicuousness, Step is as follows:
One group of pyramid of image is obtained according to described image.In order to reduce influence of the local grain to conspicuousness, this reality Apply pyramid of the example by structural map picture:A series of image collection that resolution ratio arranged with Pyramid are gradually reduced, gold Word tower bottom is that the high-resolution of pending image is represented, and top is low resolution represents.
The image to pyramidal N number of level of described image carries out Morphological Gradient treatment successively;
The image normalization of each level that will be processed by Morphological Gradient and is carried out to the original scale of described image Weighting is averaging and obtains initial conspicuousness score s'(x):
Wherein, G (Ik(x)) refer to yardstick k hypographs IkX () is after Morphological Gradient is processed and is stretched to original scale As a result, δ1And δ2Represent that Gauss standard is poor respectively;
Also demarcated by color and spatial character in view of conspicuousness, using the principle of two-sided filter, to initial notable Property score s'(x) weighting of space and color is carried out, so as to obtain final conspicuousness score s (x0):
Wherein, x0What is represented is the position of point to be calculated, and that x is represented is x0R neighborhood positions, s'(x0) that represent is x0 The initial conspicuousness score at place.
Sports ground and conspicuousness testing result are combined, Plantaginales target final score O (x) is obtained:
Chinese herbaceous peony target is analyzed according to Plantaginales target final score O (x);
Wherein, what O (x) was represented is the score of target, ξ1With ξ2It is weight coefficient,It is s (x0) knot after normalization Really,It is F (x0) result after normalization, OF (x0) be described image x0Place according to the target detection score of optical flow field, Vp is the coordinate position of the road end point, and d is the catercorner length of described image.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to assert Specific implementation of the invention is confined to these explanations.For general technical staff of the technical field of the invention, On the premise of not departing from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention by The scope of patent protection that the claims submitted to determine.

Claims (5)

1. a kind of image processing method, including road vanishing Point Detection Method step, it is characterized in that, the road vanishing Point Detection Method step Comprise the following steps:
S1, Morphological Gradient treatment is carried out to the image that vehicle front camera is obtained and obtains the first intermediate image;
S2, carries out binary conversion treatment and obtains the second intermediate image to first intermediate image;
S3, carries out Morphological scale-space and obtains the 3rd intermediate image to second intermediate image;
S4, to every a line of the 3rd intermediate image:By pixel value carry out it is cumulative obtain row pixel value and, by row pixel value and Maximum corresponding row as described image Horizon line position;
S5, carries out rim detection to being located at the parts of images below the Horizon line position in first intermediate image and obtains the Four intermediate images;
S6, straight-line detection is carried out to the 4th intermediate image and obtains the 5th intermediate image, in obtaining the 5th intermediate image Straight line;
S7, the intersection point of straight line two-by-two in the straight line obtained in obtaining step S6 determines road end point from the intersection point;
Also include Chinese herbaceous peony target detecting step, the Chinese herbaceous peony target detecting step comprises the following steps:
The image obtained according to vehicle front camera obtains one group of pyramid of the image of N number of level;
The image to pyramidal N number of level of described image carries out Morphological Gradient treatment successively;
The image normalization of each level that will be processed by Morphological Gradient and is weighted to the original scale of described image It is averaging and obtains initial conspicuousness score s'(x):
s ′ ( x ) = 1 N Σ k = 1 N G ( I k ( x ) )
Wherein, G (Ik(x)) refer to yardstick k hypographs IkThe knot of (x) after Morphological Gradient is processed and is stretched to original scale Really;
To initial conspicuousness score s'(x) weighting of space and color is carried out, so as to obtain final conspicuousness score s (x0):
s ( x 0 ) = Σ x ∈ R ( x 0 ) s ′ ( x ) · exp { - | | x - x 0 | | 2 δ 1 2 } · exp { - s ′ ( x ) - s ′ ( x 0 ) 2 δ 2 2 } ;
Wherein, x0What is represented is the position of point to be calculated, and that x is represented is x0R neighborhood positions, s'(x0) that represent is x0That locates is first Beginning conspicuousness score, δ1And δ2Represent that Gauss standard is poor respectively;
According to conspicuousness score s (x0) Chinese herbaceous peony target is analyzed;
The Chinese herbaceous peony target detecting step also comprises the following steps:
The optical flow field of described image is obtained, Chinese herbaceous peony target is analyzed according to the optical flow field;
The Chinese herbaceous peony target detecting step also comprises the following steps:
F ( x 0 ) = O F ( x 0 ) · exp { - d | | x 0 - v p | | } ,
O ( x ) = ξ 1 · s ( x 0 ~ ) + ξ 2 · F ( x 0 ~ ) ,
Chinese herbaceous peony target is analyzed according to Plantaginales target final score O (x);
Wherein, ξ1With ξ2It is weight coefficient,It is s (x0) result after normalization,It is F (x0) knot after normalization Really, OF (x0) be described image x0According to the target detection score of optical flow field, vp is the coordinate bit of the road end point at place Put, d is the catercorner length of described image.
2. image processing method as claimed in claim 1, it is characterized in that, the straight line in the 5th intermediate image is carried out as Lower treatment:
Slope screens step:Straight line of the selection slope within setting slope range;
Length screens step:Length according to straight line carries out sequence from long to short, and selection is setting the straight line before ranking.
3. image processing method as claimed in claim 2, it is characterized in that, in slope screening step, selection slope Straight line of the absolute value within [0.01,10];
After slope screens step and length screening step, also comprise the following steps:
By the absolute value of straight slope fall (i-1, i] in the range of straight line be included into in i-th straight line group:
H (i)=# i-1 < | k 'j|≤i, j=1,2 ..., N }, i=1,2 ..., 10;
Wherein, h (i) represents the number of the i-th straight line group cathetus, and N represents the total number of current screening straight line, | K'j| it is j-th strip The slope absolute value of straight line, # represent be how many bar straight slope fall (i-1, i] in;
Further according to the size of h (i), descending sort is carried out to h (i), obtain h (w) ', w=1,2 ..., 10:
Cumulative and H (r) is calculated again:
H ( r ) = Σ w = 1 r h ( w ) ′ , r = 1 , 2 , ... , 10 ;
The straight line in suitable straight line group s is chosen again:
WhereinWhat is represented is floor operation.
4. the image processing method described in claim 3, it is characterized in that, after suitable straight line group s is chosen, step S7 also includes Following steps:
The straight line that will be obtained is numbered according to the size of slope, then straight line is divided according to the odd even of sequence number, odd number Straight line collection be combined into Θodd, the straight line collection of even number is combined into Θeven, then ask for ΘoddIn any bar straight line and ΘevenIn The intersection point of any bar straight line is initial road end point, and the initial score v of initial road end point is determined by following formula The set v of (x, y):
Wherein, PiAnd PjWhat is represented respectively is the abscissa and ordinate of intersection point, and what # was represented is that how many straight-line intersection falls Position (x, y) place, what m and n was represented respectively is the length and height of described image;
Final score V (x, y) of road end point is calculated by following formula:
Φ ( i , j ) = exp { - i 2 + j 2 2 σ 2 } ;
V ( x , y ) = Σ i = - 1 l Σ j = - 1 l v ( x + i , y + j ) · Φ ( i , j ) ;
Wherein Φ (i, j) is weighted factor, and what (i, j) was represented is coordinate points on image, and σ represents that Gauss standard is poor, l representatives It is the mask size of weighting;
The corresponding pixels of V (x, y) of top score are chosen as final road end point.
5. the image processing method described in claim 1, it is characterized in that, also including Road Detection step, the Road Detection step Suddenly comprise the following steps:
To in first intermediate image be located at the Horizon line position below parts of images in texture than more consistent part It is divided into initial road region;
Convex closure treatment is carried out to the initial road region and obtains transition road area;
In the transition road area, similar pixel is polymerized to a super-pixel block;
For the super-pixel block of the transition road area adjacent edges, if in pixel in the super-pixel block, belonged to The number of transition road area is more than certain proportion, then the super-pixel block is included into the transition road area, so as to obtain Final road.
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