Clustering method for rosette scan imges

[0002] 1. Field of the Invention

[0003] The present invention relates to the clustering method for rosette scan images. In particular, the present invention relates to the method to array the image pixels obtained according to the rosette pattern in a two-dimensional memory, define partial clusters from the said memory with the array, and to generate clusters from the said defined partial clusters.

[0004] 2. Description of the Related Art

[0005] The rosette scan image is an image formed by a single element detector's scanning of the total field of view by the rosette pattern. The rosette scan image is frequently used by the infrared guided missile's detector for distinguishing the real target from false targets such as flares. The rosette seeker, through the counter-rotation of the two optical elements, provides a two-dimension scan image of a target as if an infrared detector scanned the entire field of view according to the rosette pattern.

[0006] Because a rosette seeker may obtain information regarding the size or the spatial position of the target from the detected scan image, the reaction to the target, background, clutter or to flare may be differentiated. The scanning speed of the rosette pattern is higher at the center part of petals than at the outer ends of petals. Also, more scanning lines pass the center part of the pattern than the outer parts of the pattern. Due to the difference in the scanning speed and the non-linear characteristic of the rosette pattern, the detected image differs depending on the location of the subject matter within the field of view.

[0007] Furthermore, because a rosette seeker obtains the infrared image by a single element detector's scanning, the rosette scan image has only a narrow distribution of gray scale unlike the ordinary camera image. Thus, it has been necessary to develop a signal processing method to react properly to the detected image's changes depending on the target's position and to correctly recognize targets such as flares.

[0008] The conventional rosette seeker has used the K-means clustering as a clustering method to differentiate images existing in the total field of view. However, the K-means clustering generates a different clustering result depending on the seed point of an initial cluster. Furthermore, the number of clusters must be determined prior to the initiation of the relevant algorithm. Thus, if a target discharges a random number of flares as countermeasures, the missile using the said method may fail to track the target. The ISODATA (Iterative Self Organizing Data Analysis Technique) method resolves such problems. The ISODATA clustering method, instead of specifying the number of clusters prior to the initiation of the algorithm process, determines the number of clusters while the algorithm is processed. Accordingly, regardless of the number of flares, all the clusters may be identified. However, as the seeker approaches the target, the number of detected clusters increases accordingly. Thus, values of the merging and splitting parameters must be modified frequently. Therefore, the ISODATA method has a drawback in that the processing time is extended as the relevant algorithm is repeated and the parameters must be modified during the tracking.

[0009] In order to resolve the above-described problems in the conventional clustering methods, the present invention intends to provide a clustering method to array image pixels, which have been obtained by a rosette pattern, in a two-dimensional memory and to cluster the image using the continuity of the data in the said memory, dispensing with the need for a seed point or the merging and splitting parameters.

[0010] FIG. 1 is a rosette pattern created according to N1, N2 and ΔN.

[0011] FIG. 2 is a flow chart illustrating a preferred embodiment of the clustering method for rosette scan images.

[0012] FIG. 3 is an illustration of a rosette pattern to explain the method to rearrange the rosette pattern as two-dimensional data.

[0013] FIG. 4 is an illustration of the array of image pixels into a two-dimensional memory.

[0014] FIG. 5ais an original input image;

[0015] FIG. 5bis an image in which clusters are created by the array in the two-dimensional memory; and

[0016] FIG. 5cis an illustration of the clusters in the two-dimensional memory of FIG. 5b, arrayed according to their actual coordinates.

[0017] Reference will now be made in detail to the preferred implementation of the present invention's clustering method for rosette scan images as illustrated in the accompanying drawings.

[0018] First, the rosette scan pattern will be explained with the reference to FIG. 1.

[0019] A rosette scan pattern is formed by having two optical elements rotate to the opposite directions according to certain rules with a constant rate. If rotational frequencies for two prisms are f1 and f2, the rosette pattern created therefrom may be expressed with the following Equation 1. $\begin{array}{cc}x\left(t\right)=\frac{\delta }{2}\left(\cos 2\pi f_{1}t+\cos 2\pi f_{2}t\right)y\left(t\right)=\frac{\delta }{2}\left(\cos 2\pi f_{1}t-\cos 2\pi f_{2}t\right)& \left[\mathrm{Equation}1\right]\end{array}$

[0020] In the foregoing Equation 1 δ is the refractive index of the prism.

[0021] The ratio of f₁to f₂(f₁and f₂, being the said rotational frequencies) determines the scan speed, total number of petals, width of the petal and location of the intersection points of adjacent petals. The relationship of these frequencies is as set forth in the following Equation 2. $\begin{array}{cc}\frac{N_2}{N_1}=\frac{f_2}{f_1}& \left[\mathrm{Equation}2\right]\end{array}$

[0022] In the foregoing Equation 2, N₁and N₂are positive integers and f₁is greater than f₂.

[0023] Only when the ratio of Equation 2 is always a rational number and when f₁and f₂have a greatest common measure f(N₁=f₁/f; and N₂=f₂/f), a completely closed rosette pattern may be formed according to Equation 1. In such an event, the frame frequency of the rosette pattern may be expressed with the following Equation 3. $\begin{array}{cc}T=\frac{1}{f}=\frac{N_1}{f_1}=\frac{N_2}{f_2}& \left[\mathrm{Equation}3\right]\end{array}$

[0024] The total number of petals in a rosette pattern is determined by the following Equation 4. The parameter representing the width of a petal constituting the rosette pattern is as set forth in the following Equation 5.

[0025] N=N₁+N₂  Equation 4

[0026] ΔN=N₁−N₂  Equation 5

[0027] FIG. 1aillustrates a rosette pattern where N₁is 13, N₂is 11 and ΔN is 2. FIG. 1billustrates a rosette pattern where N₁is 13, N₂is 9 and ΔN is 4. As illustrated in FIG. 1, as the value of ΔN increases, the width of a petal increases. As ΔN's value decreases, the width of a petal decreases accordingly.

[0028] FIG. 2 is a flow chart illustrating a preferred embodiment of the clustering method for rosette scan images.

[0029] As illustrated in FIG. 2, first, the subject image is obtained by a rosette pattern (21). The subject image that has been obtained by a rosette pattern is stored with different values for sample points corresponding to the gray level of such sample points. For instance, the data representing the obtained subject image may have values ranging from 0 to 255 corresponding to the gray level. According to a preferred embodiment of the present invention, the objective is not to exactly recognize the subject image but to detect the existence of a target within the subject image. A certain standard is set in order to achieve such objective. If the gray level in the subject image is higher than the standard, it is determined that a target exists and in contrast, if the gray level is lower than the standard, it is determined that a target does not exist. As a consequence, a subject image seeker level has the value 1 if an image exists or 0 if no image exists in the relevant location. In other words, the pixels corresponding to the positions where a target is detected have 1s as their values and the other pixels have 0s as their values.

[0030] FIG. 3 is an illustration of a rosette pattern to explain the method to rearrange the rosette pattern as two-dimensional data.

[0031] The image pixels obtained at the sampling times are arranged according to a non-linear pattern. Thus, such pixels have the form of one-dimensional array instead of a two-dimensional array. However, because petals in a rosette pattern are formed in the order represented by the thick solid line of FIG. 3, the continuity of pixels may not be examined with such one-dimensional array. Thus, after a pattern is completely created, the one-dimensional array for each petal is rearranged so that the relevant data may be stored in a two-dimensional memory on a two-dimensional space (22). In order to minimize the non-linear characteristic of the rosette pattern, it is recommended that a pattern, which does not have any petal over other petals in the pattern, be rearranged for such purpose.

[0032] The method to rearrange a rosette pattern will be explained in the following. First, as set forth in the following Equation 6, the number of sampling points required for forming a rosette pattern, N_T, is defined to be the amount 2 to the power of k (2^k), multiplied by 2N. The number of sampling points is made to be a multiple of 2 to the power of k in order to array the pattern into a memory space with 2^kcolumns.

[0033] N_T=2N·2^k  Equation 6

[0034] In the foregoing Equation 6, k is 1, 2 . . . , and N is the total number of petals in a rosette pattern. In order for a rosette pattern to be rearranged as a two-dimensional array, the sample time Δt must be determined according to the following Equation 7. $\begin{array}{cc}\Delta t=\frac{1}{f·N_T}& \left[\mathrm{Equation}7\right]\end{array}$

[0035] In the foregoing Equation 7, f is the frame frequency required for forming a rosette pattern.

[0036] In order to convert a rosette pattern to a two-dimensional array, each petal is divided into halves along the central line of each petal including the central point of the rosette pattern and the outer end point of the petal. The value of i for the upper half of the petal in which the rosette pattern starts to be created is 1. Then, the value of i increases one by one counterclockwise. Each row of i rows is composed of j instantaneous sampling point (N_j). Thus, the values of i and j of the relevant array are determined from the sensor's instantaneous position. The value of i corresponds to the row number and j the column number in the two-dimensional memory.

[0037] The value of i is determined by the following Equation 8. $\begin{array}{cc}i=\left[\frac{\theta \left(t\right)N}{\pi }\right]+1,\mathrm{if}\theta \left(t\right)\ge 0,i=\left[\frac{\theta \left(t\right)N}{\pi }+2\pi \right]+1,\mathrm{if}\theta \left(t\right)<0.& \left[\mathrm{Equation}8\right]\end{array}$

[0038] In the foregoing Equation 8, i ranges from 1 to 2N (i=1, 2, . . . 2N). θ(t) is the angle of the detector's instantaneous position represented with polar coordinates. Each column is composed of 2^ksamples out of the samples in the entire pattern. Thus, j ranges from 1 to 2^K(j=1,2, . . . 2^k). If j begins with the sampling point at the center of the subject pattern and ends at the outer end of a petal, the value of j may be determined pursuant to the following Equation 9.

[0039] j=(1+D)2^k−N_j+1, if Dis odd,

[0040] j=N_j−2^kD,if Dis even.  Equation 9

[0041] In the foregoing equation 9, D equals $D=\left[\frac{N_j}{2^k}\right],$

[0042] where N_j=1,2, . . . N_T.

[0043] During one cycle of the rosette scanning, the information about an object detected by an infrared sensor is stored in a memory through the functions of Equations 8 and 9. If any object is detected during the rosette scanning, the relevant memory cell of an array is filled with 1. In other cases, 0s are stored. When one cycle of scanning is completed, an array of i by j (i×j) is created in the memory. FIG. 4 is an illustration of such array of image pixels stored in a memory.

[0044] When the step of arraying the image data into a two-dimensional memory is completed as illustrated in FIG. 4, partial clusters are defined in each row (23).

[0045] Before the method to define partial clusters is explained, the meanings of the terms used in such explanation are set forth as follows.

[0046] S₁is the lth partial cluster. i is the row number and j the column number. x_ijis the pixel value of an element (i, j) in the array. n(S₁) is the number of elements included in the lth partial cluster. N_ris the minimum number of elements that one partial cluster may contain and this number is determined appropriately under the relevant circumstances.

[0047] Partial clusters are defined by determining whether there are continuous data with is as their values, beginning with the 1^strow (i.e., i=1). First, l, j and i are initialized with the value 1. Then, in the first row (i=1), the values of x_ijare examined as the value of j increases from 1 to 2^k. If x_ijhas the value 1 continuously, such element having the value 1 continuously is defined to be in a partial cluster, and i and j of such element is contained in S₁, provided that the number of such continuous 1s must be greater than the predetermined N_r. The said process of including the relevant element in S₁continues until the next pixel has the value 0. The partial cluster which is first defined in the first row becomes S₁. Partial clusters are defined for each row but more than one partial clusters may be formed in one row. As illustrated in the first row of FIG. 4, if more than one portion of a row has continuous 1s as their values, each of such portions is defined as an independent partial cluster. In FIG. 4, the first three continuous 1s in row 1 becomes S₁. The two continuous 1s that come next in the first row becomes S₂.

[0048] When the above-described process is repeated until it comes to the last row i, partial clusters such as the one in the following Equation 10 will have been defined.

[0049] S_l=[(i₁,j₁)_l(i₂,j₂)_l. . . (i_n, j_n)_l]  Equation 10

[0050] In the foregoing Equation 10, n means the number of elements contained in the lth cluster.

[0051] After partial clusters are defined as described above, it is examined whether partial clusters are adjacent to each other (24). Then, adjacent partial clusters are bound to become one independent cluster (25). According to the preferred embodiment of the present invention, the above two steps are conducted [simultaneously]. The adjacency of partial clusters is determined by examining whether an element of a partial cluster in a row is adjacent to an element of another cluster in a different row. This process is explained in detail in the following.

[0052] The universal set including all of the partial clusters is named U=[S₁, S₂. . . S_l]. An independent cluster combining adjacent partial clusters is named C_p. The examination of the partial clusters' adjacency begins with p's value 1 (p=1).

[0053] The first element of the universal set U is included in C_pand eliminated from U. Then, such condition is represented by the following Equation 11.

[0054] C_p=[S₁], U=[S₂,S₃, . . . S_l]  Equation 11

[0055] In the foregoing Equation 11, an element (i_m, j_m)_pin C_pand the lth partial cluster element (i_n, j_n)_lare examined for the adjacency according to the method represented by the following Equation 12. The lth partial element to be included in C_pis eliminated from U.

[0056] S₁εC_pand U−S₁if |(i_m,j_m)_p−(i_n,j_n)_l|=(1,0)  Equation 12

[0057] As indicated in the foregoing Equation 12, the adjacency is determined when the difference between an element included in C_pand an element of a partial cluster in U is 1. In other words, with respect to such elements, when the relevant rows are adjacent to each other and when the column number is same, the relevant partial clusters are bound into a single independent cluster. As illustrated in the foregoing Equation 12, the partial clusters determined to be adjacent to other clusters are eliminated from the universal set U.

[0058] If there is no more element in U that satisfies the condition of Equation 12, p is increased by one. This process is repeated until there is no more remaining element in U.

[0059] As illustrated in FIG. 3, in a rosette pattern, the first row and the 2Nth row (row i=1 and row i=2N) are actually adjacent to each other even though they are located apart in the memory space. Thus, the adjacency between these two rows is examined according to the following Equation 13.

[0060] C_r∪C_s, if |(i_r,j_r)−(i_s,j_s)=(2N,0)|  Equation 13

[0061] In the foregoing Equation 13, r's value is 1, 2, . . . p−1(r=1,2, . . . p−1) and s′s value is r+1, . . . p (s=r+1, . . . p) (r≠s).

[0062] When the step of examining the adjacency among partial clusters and binding adjacent partial clusters into one cluster is completed, the cluster array stored in the memory is converted into values with actual x and y coordinates. Then, the center of each cluster is determined (26).

[0063] FIG. 5ais an original input image; FIG. 5bis an image in which clusters are formed by the array in the two-dimensional memory; and FIG. 5cis an illustration of the clusters in the two-dimensional memory of FIG. 5b, arrayed according to their actual coordinates.

[0064] The step of arraying the clusters in a memory into the actual coordinates is conducted by multiplying each cluster array by the x and y array. As evidenced in FIG. 5, the present invention's clustering method may sufficiently reflect the number and the shape of the actually inputted image. The center of each cluster is determined after the clusters are rearranged in the actual coordinates as illustrated in FIG. 5c.

[0065] According to the present invention's clustering method for rosette scan images, it is not necessary to select an initial seed point as in the conventional ISODATA method or K-means method, and there is no concern about the difference in clustering results depending on the selection of the seed points. Furthermore, it is not necessary to fix the number of clusters. Also, because the clustering is conducted using the continuity of the memory number in which a pixel is stored, it is not necessary to have the merging and splitting parameters of clusters, which are necessary for the ISODATA method. Accordingly, all the clusters contained in a subject image may be separated conveniently and the calculation may be simplified.