【正文】 n mentioned above have the similar energy. The matrix method proposed extracting target’s features from SVD feature values can overe short ings of extracting SVD feature directly from matrix of the images. The experimental result shows this method has favorable stability to target matrix’s SVD feature vectors, and high invariant property to displacement , rotation and scale. It is a practical feature extracting method.Key words: Scale SVD transform。 Infrared image。 Invariant featureCLC number: T P391. 4 Document code: A Article ID: 10072276(2002) 05038703 IntroductionThe matrix singular value deposition (SVD) has been extensively applied to image pression and recognition after it was presented to solve the matrix putation by Golub and Reinch in 1970. As the singular value itself is one kind of algebraic features, the SVD is an algebraic features extracting methods. The theoretical foundation for using the singular value as the algebraic feature in image processing is its good stability. The singular value is the internal at tribute of image in essence. It is also invariant under algebraic and geometric transformations.But for the real infrared image sequence, because of the distance between sensor and object may vary in time, the size of object image will vary accordingly. If the original infrared image is directly denoted by a matrix , the stability of the singular value feature vector of this matrix will be not very good yet . A more robust and effective matrix representation of the image are needed. A feature extraction method based on the scale singular value deposition is presented to solve this problem successfully. Main ideaThe original infrared image with size is usually denoted by the matrix , but it is difficult to assure the stability of its singular value vector. In this paper, the infrared image matrix representation based on the scale transformation is adopted to satisfy the stability requirement.IR image after background elimination is shown in figure 1. Orthogonal coordinate system is shown in figure 2. Let , , and denote the coordinates of the lefttop, righttop, leftbottom and rightbottom points respectively in this orthogonal coordinate system. Then these points define a matrix which enclosures all the pixels of the object . The width , the height and the center point of this matrix are defined as , and respectively . The background of infrared image having been deleted The plane of night angle systemFirstly we draw a circle centered atwhose radiusis defined as . Let and are two positive numbers. An matrix can be constructed as followings. Beginning with zero radian angle, we travel around the circle anticlockwise. For each radius with angle , we get points with . Then the value of is selected as the gray value of the point . It’s clear that the point may be lie between two real pixels. Now we have, (1)where is a nonnegative integer and 0 q 1 , i. e. the point lies between the th and th pixels of the radius . So this paper has: (2)where and denote the gray values of th and th pixels of radius .By the above method, an matrix representation methods of the infrared image based on scale transformation is obtained. The energy of the matrices of the same kinds of object image samplings are approximate same. It is shown that using the singular value of the matrix representation presented in this paper to extract the features of the infrared image can overe the inherent disadvantage when the matrix representation of the original image is used directly . And these feature vectors can satisfy the stability definition in the sense of Frobenius norm. Experiment results and analysisThe algorithm of this paper has been implemented in the Pentium Ⅲ 600 puter and Visual C+ + environment. Its effectiveness is tested by the real infrared image. We select five kinds of planes in the experiments. The sample images of these kinds of planes are shown in figure 4. A serial of sample images of one kind of air crafts with different displacement s and rotations are shown in fig. 5. The target sample imagesLet be the training sample set of the th plane class, where is the size of training sample set , is the th infrared image sample in the set , and . The steps of feature extraction, classification and recognition of the target’s infrared images are described as followings:(1) Compute the scale transformation matrix of the infrared image .The dimension of the matrix is . The target multure sample images(2) Compute the average image of the infrared images of the th plane class, w here: (3) The target sample images after rotation transformation(3) Compute the SVD of the matrix to obtain the infrared images’ singular value feature vector .(4) Classify the plane infrared images based on the minimal distance criteria. Let is an object image, its scale transformation matrix is , ’s singular vector feature vector is . T he recognition criteria can be described as following, if:,where ,then .In the experiments, the sample image number of each class is selected as 100, so the total number of the sample image is 500. Randomly select 50 training sample images from the sample image set of each object class, so we have 250 training sample images in total. The left 250 sample images are used as test samples. The dimension of matrix is . The recognition accuracy rates of six randomly selected classification experiments are %、%、%、%、%、%. The average recognition accuracy rate is % . We have also designed the experiments which directly use the matrix representation of original infrared image to do the feature extraction and average recognition accuracy rate of the six randomly selected experiments is %.The two numbers show the effectiveness of our method. ConclusionsThe stabil