CN100344947C - Similarity measurement method based on spectrum polygon - Google Patents
Similarity measurement method based on spectrum polygon Download PDFInfo
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- CN100344947C CN100344947C CNB2003101093486A CN200310109348A CN100344947C CN 100344947 C CN100344947 C CN 100344947C CN B2003101093486 A CNB2003101093486 A CN B2003101093486A CN 200310109348 A CN200310109348 A CN 200310109348A CN 100344947 C CN100344947 C CN 100344947C
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- spectral
- polygon
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- area
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Abstract
The present invention relates to a similarity measurement method based on a spectrum polygon, which belongs to the technical field of remote sensing information processing and application technologies. The present invention is based on the set theory and the set operation and combined with the characteristics of a spectral curve. The spectral curve is expressed by establishing the spectral polygon. Moreover, set area processing is carried out for the spectral polygon under two uniform coordinate systems so as to obtain an index of similarity measurement. The present invention comprises three procedures: establishing the spectral polygon through a process that the spectral curve, two vertical lines which pass through the wavelength of a first waveband and a last waveband and are perpendicular to a transverse axis, and the transverse axis form a polygon to obtain the spectral polygon; implementing the set operation of the spectral polygon through a process that the value of an area is used as a quantification function for carrying out quantization description for a new set generated by two spectral polygon sets through the set operation to obtain an area index through the spatial relation between trapezoids formed by decomposing the spectral polygon; obtaining a similarity measurement factor through a process that a measurement index mu 1 is obtained according to the characteristics of similarity and diversity. The present invention can enhance the precision and the reliability of the measurement.
Description
Technical field
The present invention relates to a kind of method for measuring similarity, particularly a kind of method for measuring similarity based on spectral polygon.Belong to areas of information technology.
Background technology
Spectrum vector similarity measurement problem in the processing such as target in hyperspectral remotely sensed image classification, information extraction, retrieval, coupling has proposed many metric algorithm over nearly 20 years, comprise Euclidean distance, spectrum angle, related coefficient, SID etc.Distance method and spectrum angle mainly are based on geometric theory, as a definite type data set, are subjected to the stochastic error and the The noise that may occur bigger the spectrum vector, and insensitive to local feature in higher dimensional space; Related coefficient, SID etc. are based on probability theory, and spectrum work amount as a random vector, can be adapted to the requirement of mixed pixel, but the distribution and the shape of its effect and spectrum vector are closely related, and the hypothesis of random vector might not be set up sometimes.Find by literature search, Chein_IChang is at " IGARSS ' 99Proceedings.IEEE 1999International " (IEEE 1999 geoscience and remote sensing proceeding), Volume:1, " the Spectral Information Divergence for Hyperspectral Image Analysis " that delivers on the 28June-2July 1999Page:509-511 (the spectral information divergence in the Hyperspectral imaging analysis), but the method for using only is from the reflectivity dimension spectrum vector to be considered, and do not consider the characteristics of wavelength dimension and the corresponding relation of reflectivity and wavelength, be a kind of one dimension measure in essence, the accuracy of measurement and reliability are not satisfactory.
Summary of the invention
The object of the invention is the deficiency at existing spectral similarity measure, a kind of method for measuring similarity based on spectral polygon is proposed, make it will gather similarity measure operation and the theoretical spectrum vector similarity measurement field of introducing, when being effective to similarity measurement, reduce the susceptibility of tolerance result, can improve the accuracy of measurement and reliability error.
The present invention realizes by following technical scheme, the present invention is based on set theory and set operation, characteristics in conjunction with the curve of spectrum, employing is set up spectral polygon and is expressed the curve of spectrum, the processing that spectral polygon under two unified coordinate system systems is gathered area again, obtain the similarity measurement index, specifically comprise and set up spectral polygon, implement the spectral polygon set operation, obtain three basic steps of the similarity factor:
(1) sets up spectral polygon: with the curve of spectrum, cross first wave band and last wave band wavelength and constitute a polygon, promptly obtain spectral polygon perpendicular to two pedal line and the transverse axis of transverse axis;
(2) implement the spectral polygon set operation: as quantization function, set is carried out quantificational description through the new set that set operation generates to two spectral polygons with area, resolves into by spectral polygon and trapezoidally obtains area index with the trapezoid space relation;
(3) obtain the similarity measurement factor: according to the characteristics of similarity and diversity, attainment degree figureofmerit μ 1 can realize spectral similarity tolerance effectively.
The present invention can measure the similarity of spectrum vector preferably, and the tolerance result is subjected to feature drift, error effect less, can realize the reliable tolerance to spectral similarity in the high-spectrum remote-sensing.
Below the present invention is done further qualification, particular content is as follows:
1, sets up spectral polygon
Each spectrum vector can be that transverse axis, reflectivity are that the curve of spectrum of the longitudinal axis is expressed in order to wavelength, the spectrum vector is corresponding with the curve of spectrum, therefore with the curve of spectrum, cross first wave band and last wave band wavelength and constitute a polygon perpendicular to two pedal line and the transverse axis of transverse axis, be called spectral polygon.Different atural objects or picture dot have the different curves of spectrum, and corresponding have different spectral polygons.Thereby two spectrum vector similarity measurement problem is converted to the similarity measurement problem of two spectral polygons under the unified coordinate system.
2, implement the spectral polygon set operation
Regard two spectral polygons as two spatial aggregation A and B under the unified coordinate system, the function that definition geometric figure area function M (X) quantizes for pair set.According to set theory and set operation, can obtain two intersection of sets collection quantizating index M
1=M (A ∩ B), belong to A but do not belong to the set quantizating index M of B
2=M (A ∩ B), belong to B but do not belong to the scope quantizating index M of A
3The quantizating index M of=M (A ∩ B), A and B union
7=M (A ∪ B)=M
1+ M
2+ M
3Obtaining when respectively gathering area, although spectral polygon is irregular, but can be with it as by N-1 (wherein N is the wave band number) individual trapezoidal composition, each is trapezoidal by adjacent two wave band place wavelength, reflectivity decision, obtain the area of sub-spectral polygon more one by one, obtain the area index that needs after adding up.
These indexs are delineated the relation of the difference between two set, can obtain the similarity measurement index based on this.
3, obtain the similarity factor
By combination and analysis to seven quantizating index in front, can obtain the similarity measurement factor, the key index of wherein weighing similarity is M
1I.e. quantized value of Jiao Jiing, the ratio that adopts two spectral polygon set A, B common factor area and union area among the present invention can through type μ as the similarity measurement factor
1=M
1/ M
7Obtain, its codomain is [0,1], gets 1 when A, B are complete when similar, does not get 0 simultaneously fully.
The key of weighing diversity is M
2And M
3, i.e. the area of two spectral polygon differences (not overlapping) parts, the present invention adopts the ratio of two spectral polygon set difference value part areas and union area as the diversity measure coefficient, can through type d
1=(M
2+ M
3)/M
7=1-μ
1Obtain.
According to the characteristics of similarity and diversity index, the two is divided by obtains the comprehensive similarity measurement factor, can use formula
Obtain.This factor is big more, represents that the similarity of the entity that two set are represented is high more.When two vectorial when in full accord, this index value is infinitely great.
Because s
1, d
1And μ
1Be to be mutually related, just can obtain other two factors by some factors, so the present invention select μ
1As the final similarity measurement factor, work as μ
1Thought that two spectrum vectors were similar at＞0.9 o'clock, can be included into same class.
The present invention has used spectral polygon as the feature representation mode, when considering spectral properties value (reflectivity), wavelength has been carried out synchronous consideration, carry out similarity measurement from two-dimensional space, avoid traditional algorithm only to consider the defective of spectral properties, can either be applied to pure picture dot, can be used in mixed pixel again, can satisfy the requirement of target in hyperspectral remotely sensed image, object spectrum curve similarity measurement, have better anti-difference performance than traditional algorithm; The present invention has used set theory, classical feature contrast model and two-dimensional space solid similarity measurement, can avoid traditional algorithm to depend on the shortcoming of vector distribution and probability function, overcome the characteristics that traditional algorithm is only considered the reflectivity dimension, ignored Wavelength distribution, it mainly calculates is exactly that area calculates, realize comparatively simple, be a kind of effectively, reliably, spectrum vector method for measuring similarity fast; The present invention can be used for the similarity measurement of high-spectrum remote-sensing spectrum vector, specifically comprises aspects such as target in hyperspectral remotely sensed image classification, retrieval, typical target identification, change detection.
Embodiment
For understanding technical scheme of the present invention better, below provide specific embodiment.
Based on two curves of spectrum to be measured, after forming two spectral polygons respectively, two spectral polygons have different spatial relationships in the different-waveband position in wavelength-reflectivity coordinate system, with per two adjacent band is that research object is considered the trapezoidal spatial relationship that two spectral polygons form on corresponding wave band, can calculate corresponding common factor and difference set area index M at each situation
1=M (A ∩ B), M
2=M (A ∩ B) and M
3=M (A ∩ B).Concrete grammar is as follows:
(1) two trapezoidal be relation of inclusion, trapezoidal A is comprised among the trapezoidal B, A satisfies condition
i＜B
iAnd A
I-1＜B
I+1, M occurs simultaneously this moment
1Area is exactly the area of A; The common factor M of A and B
2Be empty set, its quantized value is 0; The common factor M of A and B
3Deduct the area of A for the area of B.
(2) A, B two are trapezoidal is overlapping relation, and A satisfies condition
i＜B
iAnd A
I+1＞B
I+1, obtain the each several part area, at first to determine the coordinate (λ of intersection point place according to straight-line equation
0, ρ
0), M then occurs simultaneously
1Area realize available formula M by two little trapezoidal area sums
1=(ρ
0+ A
i) * (λ
0-λ
i)/2+ (ρ
0+ B
I+1) * (λ
I+1-λ
0)/2 expression; The common factor M of A and B
2Realize by the little triangle area in right side, use formula M
2=(A
I+1-B
I+1) * (λ
I+1-λ
0)/2 expression; The common factor M of A and B
3Area i.e. the little triangle area in left side, uses formula M
3=(B
i-A
i) * (λ
0-λ
iCalculate)/2.
(3) A and B are still relation of inclusion, but different with (1), are that A comprises B at this moment, and A satisfies condition
i＞B
iAnd A
I+1＞B
I+1, M occurs simultaneously this moment
1Area is exactly the area of B; The common factor M of A and B
2It is the area that the area of A deducts B; The common factor M of A and B
3Be empty set, its quantized value is 0.
(4) A, B two are trapezoidal is overlapping relation, and opposite with the overlapping relation of (2), A satisfies condition
i＞B
iAnd A
I+1＜B
I+1Obtain the each several part area, at first will determine the coordinate (λ of intersection point place according to straight-line equation
0, ρ
0), M then occurs simultaneously
1Area calculate two little trapezoidal areas and realization, use formula M
1=(ρ
0+ B
i) * (λ
0-λ
i)/2+ (ρ
0+ A
I+1) * (λ
I+1-λ
0Express)/2; The common factor M of A and B
2Promptly the little leg-of-mutton area in left side is used formula (A
i-B
i) * (λ
0-λ
i)/2 expression; The common factor M of A and B
3Area is the little triangle area in right side, uses formula M
3=(B
I+1-A
I+1) * (λ
I+1-λ
0)/2 obtain.
According to above method, two spectral polygons all are divided into N-1 trapezoidal (N is the wave band number) by adjacent band, obtain out each trapezoidal middle each several part area successively, obtain the area index of needs after adding up, just can obtain similarity and diversity metric, the similarity measurement factor, with the similarity of tolerance spectral polygon, and then as the metric of curve of spectrum similarity.
From certain target in hyperspectral remotely sensed image, selected three class atural objects, two picture dots of every class to calculate, the index μ of table 1-table 3 for measuring based on set theory and spectral polygon
1, μ
2, s the result.
Table 1 calculates μ based on the area similarity
1
| μ 1 | ||||||
| A1 | A2 | B1 | B2 | C1 | C2 | |
| A1 | 1 | 0.77 | 0.74 | 0.76 | 0.65 | 0.61 |
| A2 | 0.77 | 1 | 0.73 | 0.7 | 0.57 | 0.52 |
| B1 | 0.74 | 0.73 | 1 | 0.76 | 0.65 | 0.59 |
| B2 | 0.76 | 0.70 | 0.76 | 1 | 0.68 | 0.63 |
| C1 | 0.65 | 0.57 | 0.65 | 0.68 | 1 | 0.81 |
| C2 | 0.61 | 0.52 | 0.59 | 0.63 | 0.81 | 1 |
Table 2 calculates μ based on the area similarity
2
| μ 2 | ||||||
| A1 | A2 | B1 | B2 | C1 | C2 | |
| A1 | 1 | 0.9 | 0.87 | 0.88 | 0.81 | 0.77 |
| A2 | 0.9 | 1 | 0.85 | 0.83 | 0.78 | 0.72 |
| B1 | 0.87 | 0.85 | 1 | 0.87 | 0.85 | 0.77 |
| B2 | 0.88 | 0.83 | 0.87 | 1 | 0.85 | 0.80 |
| C1 | 0.81 | 0.78 | 0.83 | 0.85 | 1 | 0.91 |
| C2 | 0.77 | 0.72 | 0.77 | 0.80 | 0.91 | 1 |
Table 3 calculates s based on the area similarity
| s＝μ 1/d 1 | ||||||
| A1 | A2 | B1 | B2 | C1 | C2 | |
| A1 | ∞ | 3.32 | 2.86 | 3.12 | 1.87 | 1.57 |
| A2 | 3.32 | ∞ | 2.66 | 2.31 | 1.33 | 1.10 |
| B1 | 2.86 | 2.66 | ∞ | 3.13 | 1.88 | 1.46 |
| B2 | 3.12 | 2.31 | 3.13 | ∞ | 2.16 | 1.68 |
| C1 | 1.87 | 1.33 | 1.88 | 2.16 | ∞ | 4.27 |
| C2 | 1.57 | 1.10 | 1.46 | 1.68 | 4.27 | ∞ |
In order to analyze to using effect, be example with a certain curve of spectrum c, retrieval and its coupling from 50 curves of spectrum, wherein curve d is the object spectrum curve similar with c, other curve is inhomogeneous.Get the curve of similarity measurement index s for the first five, corresponding index is as shown in table 4.
Table 4 is by the first five items result for retrieval of two kinds of method for measuring similarity couplings
| Similarity measurement based on area | |||||
| I | II | III | IV | V | |
| Desired value | ∞ | 4.27 | 3.18 | 2.63 | 1.94 |
| The curve numbering | c | d | q | x | y |
Result for retrieval is analyzed, and in based on area tolerance, first occurrence is this curve itself, and second occurrence is to represent another similar picture dot curve of spectrum of atural object with this curve, and three of back are other atural object class curve of spectrum.
In addition, also this method and traditional measure method----spectrum angle are compared.The result shows: when being used for similarity measurement, similar curves is had higher ratio of similitude based on the method for spectral polygon, for different curves, index is then on the low side, and its performance and effect comprehensively are better than classic method.
Claims (4)
1, a kind of method for measuring similarity based on spectral polygon, it is characterized in that, based on set theory and set operation, characteristics in conjunction with the curve of spectrum, employing is set up spectral polygon and is expressed the curve of spectrum, the processing that two unified coordinate system system spectral polygon is down gathered area obtains the similarity measurement index again, specifically comprises setting up spectral polygon, the set operation of enforcement spectral polygon, obtaining three basic steps of the similarity factor:
(1) sets up spectral polygon: with the curve of spectrum, cross first wave band and last wave band wavelength and constitute a polygon, promptly obtain spectral polygon perpendicular to two pedal line and the transverse axis of transverse axis;
(2) implement the spectral polygon set operation: as quantization function, set is carried out quantificational description through the new set that set operation generates to two spectral polygons with area, resolves into by spectral polygon and trapezoidally obtains area index with the trapezoid space relation;
(3) obtain the similarity measurement factor: according to the characteristics of similarity and diversity, attainment degree figureofmerit μ
1, realize spectral similarity tolerance.
2, the method for measuring similarity based on spectral polygon according to claim 1 is characterized in that, in the step (2), implements the spectral polygon set operation, and is specific as follows:
As two spatial aggregation A under the unified coordinate system and B, the function that definition geometric figure area function M (X) quantizes for pair set according to set theory and set operation, obtains two intersection of sets collection quantizating index M with two spectral polygons
1=M (A ∩ B), only belong to the set quantizating index M of A
2=M (A ∩ B), only belong to the scope quantizating index M of B
3The quantizating index M of=M (A ∩ B), A and B union
7=M (A ∪ B)=M
1+ M
2+ M
3, obtaining when respectively gathering area, as by N-1 trapezoidal the composition, wherein N is the wave band number with it, each is trapezoidal by adjacent two wave band place wavelength, reflectivity decision, obtains the area of sub-spectral polygon more one by one, obtains area index after adding up.
3, the method for measuring similarity based on spectral polygon according to claim 1 is characterized in that, in the step (3), obtains the similarity factor, and is specific as follows:
M
7Be the quantizating index M that two set A and B occur simultaneously
1, belong to A but do not belong to the quantizating index M of the set of B
2With belong to B but do not belong to the quantizating index M of the set of A
3Sum; The key index of weighing similarity is that the quantized value that occurs simultaneously is M
1, the ratio that adopts two spectral polygon set A, B common factor area and union area is as the similarity measurement factor, through type μ
1=M
1/ M
7Obtain, its codomain is more than or equal to 0 and smaller or equal to 1, gets 1 when A, B are complete when similar, gets 0 when different fully, and the key of weighing diversity is M
2And M
3, i.e. the area of two spectral polygon differences parts, the ratio that adopts two spectral polygon set difference value part areas and union area be as the diversity measure coefficient, through type d
1=(M
2+ M
3)/M
7=1-μ
1Obtain, according to the characteristics of similarity and diversity index, the two is divided by obtains the comprehensive similarity measurement factor, uses formula
Obtain, this factor is big more, represents that the similaritys of entity of two set representatives are high more, and when two vectorial when in full accord, this index value be an infinity.
4, the method for measuring similarity based on spectral polygon according to claim 3 is characterized in that s
1, d
1And μ
1Be to be mutually related, can obtain other two factors, select μ by some factors
1As the final similarity measurement factor, work as μ
1Thought that two spectrum vectors were similar at＞0.9 o'clock, be included into same class.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2002041530A (en) * | 2000-07-24 | 2002-02-08 | Nippon Telegr & Teleph Corp <Ntt> | Retrieval method of three-dimensional body database and recording medium having retrieving program for three-dimensional body database recorded thereon |
| JP2002181560A (en) * | 2000-12-08 | 2002-06-26 | Matsushita Electric Ind Co Ltd | Transfer method for polygon information and apparatus for executing it |
| US6532304B1 (en) * | 1998-10-21 | 2003-03-11 | Tele Atlas North America, Inc. | Matching geometric objects |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6532304B1 (en) * | 1998-10-21 | 2003-03-11 | Tele Atlas North America, Inc. | Matching geometric objects |
| JP2002041530A (en) * | 2000-07-24 | 2002-02-08 | Nippon Telegr & Teleph Corp <Ntt> | Retrieval method of three-dimensional body database and recording medium having retrieving program for three-dimensional body database recorded thereon |
| JP2002181560A (en) * | 2000-12-08 | 2002-06-26 | Matsushita Electric Ind Co Ltd | Transfer method for polygon information and apparatus for executing it |
Non-Patent Citations (1)
| Title |
|---|
| Location similarity of regions stephen winter,Photogrammetry & remote sensing,Vol.55 2000 * |
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