Nuevos géneros y formatos

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DIGITAL IMAGE DATA

IMAGE RESTORATION AND ENHANCEMENT

PRE CLASSIFICATION SITE VISITS

ADOPTION OF CLASSIFICATION SCHEME

GROUND TRAINING OVER

TRUTHING REPRESENTATIVE AREAS

SUPERVISED CLASSIFICATION POST-PROCESSING AND ACCURACY ASSESSMENT

Fig. 2.3: Procedure for supervised classification (Igbokwe, 2005)

42 Classification algorithm includes (i) Parallelepiped classification algorithm

The parallelepiped algorithm is a computationally efficient method of classifying remote sensor data. Unfortunately, because some parallelepipeds overlay, it is possible that an unknown candidate pixel might satisfy the criteria of more than one class. In such cases it is usually assigned to the first class for which it meets all criteria. A more elegant solution is to take the pixel that can be assigned to more than one class and use a minimum distance to mean decision rule to assign it to just one class (Khatibi, 2015).

The parallelepiped classifier uses the class limits stored in each class signature to determine if a given pixel falls within the class or not; the class limits specify the dimension (in standard deviation units) of each side of a parallelepiped surrounding the mean of the class in feature space. If the pixel falls inside the parallelepiped, it is assigned to the class. However, if the pixel falls within more than one class, it is placed in the overlap class (code 255). If the pixel does not fall inside any class, it is assigned to the null class (code 0).

The parallelepiped classifier is typically used when speed is required. The drawback is (in many cases) poor accuracy and a large number of pixels classified as ties (or overlap, i.e class 255).

(ii) Minimum Distance to mean classification Algorithm

The decision rule is computationally simple and commonly used. When used properly it can result in classification accuracy comparable to other more computationally intensive algorithms, such as the maximum likelihood algorithm.

Like the parallelepiped algorithm, it requires that the user provide the mean vectors for each class. To perform a minimum distance classification, a program must calculate the distance to each mean vector. From each unknown pixel, it is possible to

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calculate this distance using Euclidean distance based on the Pythagorean Theorem.

The computation of the Euclidean distance from point to the mean of class measured in band relies on the equation (2.10) according to (Khatibi, 2015).

Dist = SQRT ( (BVijk – ck) + (BVijl – cl)) ...(2.10) Where ck and ci represent the mean vectors for class c measured in bands K and L.

BVijk – Matrix in Band K BVijl – Matrix in Band L

Minimum distance classifies image data on a database file using a set of 256 possible class signature segments as specified by signature parameter. Each segment specified in signature for example, stores signature data pertaining to a particular class. Only the mean vector in each class signature segment is used (Khatibi, 2015).

(iii) Fisher classification

Is one of the simplest classification algorithms. The method finds a direction W in the N dimensional space. The Fisher classifier calculates the projection of the sample onto W, the idea is to find a direction which after projecting will maximize interclass variability and minimize intraclass variability. It can be achieved by maximizing the following function in equation (2.11).

J(w)= m1 – m2 2

...(2.11)

Where m1 and m2 are the mean value of the projected positive and negative samples respectively. s1 and s2 are the standard deviations of the projected samples.

In the simple two-dimensional case, after the points are projected onto the line, the two classes are transformed into two sets of points upon the line. The interclass variability in this case is the distance between the class centers and the intraclass

S2 1 + S22

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variability is the distance of class members from their class centers. Different criteria can be employed to determine the class for a new sample, by Calculating the distance from the point to the means of the projected training classes and adding a weighing scheme in order to minimize the bias caused by the relative sizes of the training classes. The advantage of fisher’s classification is that the vector w can be found swiftly using a simple procedure (Pereira et al., 2012).

(iv) Maximum likelihood classifier

Is one of the most popular methods of classifications in remote sensing, in which a pixel with the maximum likelihood is classified into the corresponding class.

The likelihood is defined as the posterior probability of a pixel belonging to class K (Pereira et al., 2012)

Lk =P(k/x ) = P (k) * P(x/k)/EP(i) * P(x/i) … (2.12) Where P(k) - prior probability of class K

EP(i) – Exponential of (i)

P(x/k) --- conditional probability to observe X from class k or probability density functions.

P(x/i) – Conditional Probability to observe x from class i

Usually P(k) are assumed to be equal to each other and EP(i) * P(x/i) is also common to all classes. Therefore L_K depends on P(x/k) or the probability density function.

For mathematical reasons, a multivariable normal distribution is applied as the probability density function. In the case of normal distributions, the likelihood can be expressed as follows:

L_k(x) = ¹

2𝜋^𝑛₂ /𝜀𝑘/¹₂ exp ¹/₂(x-_k) Ʃ_k^-1 (x-_c)^t ...(2.13)

45 Where n-number of bands

X image data of n bands

L_k(x) likelihood of x belonging to class K k - mean vector of class K

c – mean vector of another class

Ʃk variance - covariance matrix of class K /Ʃ_k

/

The maximum likelihood has an advantage from the view point of probability theory, but care must be taken with respect to the following items

(i) Sufficient ground truth data should be sampled to allow estimation of the mean vector and the variance covariance matrix of population

(ii) The inverse matrix of the variance covariance matrix becomes unreliable when very high correlation exists between two bands. In such cases, the number of bands should be reduced by a principal component analysis.

(iii) When the distribution of the population does not follow the normal distribution, the maximum likelihood method cannot be applied.