Use of Chain Code Histogram Method to Quantify Airborne Particle Shapes

Transcription

1 Aerosol Science and Technology ISSN: (Print) (Online) Journal homepage: Use of Chain Code Histogram Method to Quantify Airborne Particle Shapes Ying Xie, P. K. Hopke, Gary Casuccio & Brad Henderson To cite this article: Ying Xie, P. K. Hopke, Gary Casuccio & Brad Henderson (1994) Use of Chain Code Histogram Method to Quantify Airborne Particle Shapes, Aerosol Science and Technology, 21:3, , DOI: / To link to this article: Published online: 12 Jun Submit your article to this journal Article views: 355 View related articles Citing articles: 3 View citing articles Full Terms & Conditions of access and use can be found at

2 Use of Chain Code Histogram Method to Quantify Airborne Particle Shapes Ying Xie and P. K. Hopke* Chemistry Department, Clarkson University, Potsdam, NY Gary Casuccio and Brad Henderson R. J. Lee Group Inc., 350 Hochberg Road, Monroeuille, PA The chain code histogram method was used to provide a shape index to characterize airborne particles. A total of 136 airborne particles were analyzed using this method. The results showed that the chain code histogram method is an easy and quick way to quantify airborne particle shapes. Furthermore, this technique has the potential to be incorporated into the on-line Computer-Controlled Scanning Electron Microscope (CCSEM) analysis software such that a simple shape index can be determined in automatic fashion along with the particle size, elemental chemistry and image. INTRODUCTION Airborne particles play a very important role in air quality with resulting problems on public health. In order to make effective control strategies, studies of particle composition, sources, and transportation are needed. Receptor models based on single particle classification have proven to have high specificity for source identification and airborne particle mass apportionment (Kim and Hopke 1988a, 1988b). However, these models depend directly on the ability to classify particles into well defined classes. Thus, particle classification is a critical first step in the use of single particle receptor models. Currently, particle classification has been performed based only on the chemical information obtained from the fluoresced x-rays. However, some particles may share very similar chemical composition but come from different sources. For *Author to whom correspondences should be addressed. example, fly ash and clay mineral particles may share very similar chemical compositions. However, they have quite different shapes. Fly ash particles are spherical because they experience high temperatures while clay mineral particles are nonspherical because they are from mechanical processes. In order to develop effective pollution control strategies, it is important to distinguish between these two sources. The fly ash particles are from combustion processes. They clay mineral particles are crustal material from natural sources. Thus, there is a need to combine a shape index with the chemical compositions so that more accurate particle classification can be achieved. In receptor modeling studies based on the characterization of individual particles, most of the particles can be distinguished by their chemical compositions. The most difficult problem is to distinguish fly ash and clay mineral particles. Thus, the problem is to define a shape index that can clearly discriminate spherical particles from nonspherical ones. Aerosol Science and Technology 21: (1994) D 1994 Elsevier Science Inc.

3 Use of Chain Code Histogram Method 211 Chain code generation is the technique used to follow the boundary of an object as well as creating a record of the path followed as the object's outline is defined. In general, a chain code describes the direction to move from the current pixel to the next boundary pixel. As shown in Figure 1, the chain code is a data array that stores the ordered representation of the eight possible directions of the boundary pixels. The eight directions are numbered from 0 to 7. The frequency distribution of the occurrence of the various directions reflect the shape of the object. The normalized histogram is size invariant and the changes in the orientation of the object are equivalent to horizontal cyclic shifts in the histogram (Sadjadi (1992). Sadjadi used the chain code histogram method to perform object recognition. He suggested that the chain code histogram may provide shape information and a chain code histogram library may be created. Then, any unknown object can be recognized by matching its chain code histogram with the ones in the library. As an initial study of the utility of chain code histograms, airborne particle images obtained using Computer-Controlled Scanning Electron Microscope (CCSEM) were first preprocessed such that the binary images were obtained; a binary image means all the foreground picture elements (pixels) equal to a nonzero value and all the background pixels equal to zero. Based on the binary images, the chain code histograms of the particle images were generated. The chain code histogram patterns were then studied to determine if spherical particles could be easily distinguished from the non-spherical particles. IMAGE PREPROCESSING The particle images were taken using CCSEM with a 1 byte/pixel resolution. Thus, they are images with pixel values * Starting Point FIGURE 1. Definition of the chain code and an example of the chain code of an image. ranging from 0 to 255. Figure 2 shows a typical image obtained using CCSEM. The present CCSEM system can find the edge points easily based on the contrast between the particle and the background. The only work that needs to be conducted is to store the edge points as the codes defined for the directions. Then the chain

4 2 Y. Xie et al. 2. A particle image taken by CCSEM. Pixel Value code histogram can be generated. Thus, '.here would not be a preprocessing of the image if this method were incorporated into the on-line system. However, at this exploratory stage, the method needs to be developed in an off-line mode. Thus, there is a need to employ image preprocessing to separate the foreground from the background. Because only the foreground pixels were of interest, the first step was to separate foreground from background. Thresholding can achieve this. Figure 3 shows the histogram of the particle image shown in Figure 2. Thus, a threshold at the pixel value of 70 was selected for this particle. After thresholding, the image shown in Figure 4 was obtained and its histogram is shown in Figure 5. It can be noted that there are some small black holes in the foreground region and also there is some noise in the background region. Thus, there is a nced to remove the noise in the background region and fill the holes in the foreground region. To achieve this, the shrink and swell filters were used. In this study 5, was used as the filter index FIGURE 3. The histogram of the image shown in Figure 2. ters. It is a binary image without noise and holes. In order to show the effect of the filter index value, Figure 7 shows the image with shrink filter index of 5 and the swell filter index of 4. Comparing Figures 6, 7, and the original image shown in Figure 2, it can be noted that Figure 7 has a greatly distorted edge and results in an image that no longer resembles the origi- for all the particles. Figure 6 shows the FIGU 4. The image after thresholding of Figfinal image after the shrink and swell fil- ure 2.

5 Use of Chain Code Histogram Method Pixel Value 5. The histogram of imagc shown in Figure The resulted image after using the shrink filter with index of 5 and swell filter with index of 4. nal particle shape. Thus, care must bc taken in choosing the filter index. GENE CODE Once the binary image is obtained, the chain code of the boundary may bc generated. The algorithm for generating chain GURE 6. The resulted imagc after using the shrink and swell filters with both filter index of 5. code is as follow: Stcp 1: Find a pixel on the boundary of the foreground region; Step2: Store the starting pixel's location; Step3: Examine each neighbor in a counter-clockwise direction until a forcground pixel is found; Step4: Save the chain link according to the definition in Figure 1; Step5: Let the new pixel of the interest be the neighbor found in step 3. If the pixel of interest is not the starting pixel, go to step 3; otherwise stop. The chain code for the forcground boundary can be generated easily following this owever, one problem remains. In step 3, every neighbor is checked in order to find the foreground neighbor and some of them may then be checked more than once from differing pixels resulting in lost computing time. In order to avoid this repetition problem, a closedform expression was derived (shown as Eq. 1) to determine which neighbor should be examined first without looking at pixels that had already been searched.

6 214 Y. Xie et ai. [ (last 1i;k + 6) start link = 2 mod I (1) where start link is the coded direction from current pixel to the one that should be examined, and it is coded from 0 to 7 as defined in Figure 1. Similarly, last link is the coded direction from the previous interesting pixel to the current pixel of interest. The operator "mod7' generates the remainder. After the chain code of the boundary was generated, its histogram can be calculated by counting the frequencies corresponding to every chain code number that is from 0 to 7. The normalized histogram is generated by dividing the frequencies by the total number of the edge pixels. The normalized histogram is image size invariant. Figure 8 shows the normalized chain code histogram of the particle shown in Figure 2. APPLYING THE CHAIN CODE HISTOGRAM METHOD TO DISTINGUISH SPHERICAL PARTICLES FROM NONSPHERICAL PARTICLES The concept of the chain code histogram suggests that a spherical shape should have a uniform chain code histogram with the frequency for each of the chain code values of 1/8. However, when an image is digitized, all eight possible directions do not have the same probability. The vertical and horizontal directions have somewhat higher probabilities than the diagonal directions. This discrepancy can be understood as follows: A quantized description of an edge is obtained by designating as edge points the coordinates of the grid nodes that lie close to the given edge. The edge points are connected in sequence by diagonal, horizontal, or vertical straight-line segments to approximate the edge. This is shown in Figure 9. There are various kinds of quan t I I I I I Chain Code FIGURE 8. The normalized chain code histogram of the image shown in Figure 2. tization schemes to estimate the probability for each direction. However, a diamond shape should be used for an 8-directional digitized image. This is called grid-intersect quantization (Koplowitz 1981; Freeman 1974). The diamond shape is formed by connecting the mid-points of the 4 grid lines that define the 4 adjacent pixels. Suppose the edge being digitized is straight over a small distance, then intersecting the cross in the diamond (Figure FIGURE 9. Grid-intersect quantization of 8-directional digitized image.

7 Use of Chain Code Histogram Method 9) is equivalent to intersecting the diamond at any point. The probability of horizontal direction is equal to: and where P(A) and P(B) are the probabilities for the edge intersecting diamonds A and B, respectively. P( A) = P(B) = perimeter of the diamond, and P(B ua) equals to the perimeter of the whole convex hull formed by the two diamonds. Suppose the unit length of the pixel cell is 1, then and Combining Eqs. 2 and 3, P(B/A) = 1 - n /2 = The probability for both horizontal and vertical directions are 0.293; thus, the probability for the diagonal direction is 1-2"0.293 = Finally, the probability for each horizontal and vertical direction is 0.293/2 = 0.147, and the probability for each diagonal direction is 0.414/4 = From this discussion, it can be concluded that the probability for a diagonal direction is smaller than for a horizontal or vertical direction. It should be noted that the diagonal directions were represented by odd numbers in the chain code while the vertical and horizontal directions werc represented by even numbers. This results in the chain code histogram for a spherical object showing an odd-even effect. The solid line in Figure 11 is the odd-even chain code histogram of the spherical particle shown in Figure 10. After dividing the frequencies by and for odd-number coded directions FIGURE 10. A spherical particle image taken by CCSEM. and even-number coded directions, respectively, the histogram is closer to being a straight line as the dotted line shown in Figure 11. The criteria for spherical particle shape are that first, the normalized chain code histogram should have a zig-zag pattern. Secondly, the minimum frequency among the 8 directions should be greater than a. Original. Modified I Chain Code CURE 11. The chain code histogram for the image shown in Figure 10.

8 Y. Xie et al. LE 1. Frequencies of Chain Codcs for Some Rcgular Shapes Chain Codc Rectangular Hexagon Octagon Nonag on threshold, for example, in this study was used. The zig-zag pattern can be recognized by computing the difference of the slope of two neighbor lines in the histogram. If the absolute value of difference is bigger than both of the two absolute slopes, then these two neighbor lines have the opposite slope. If this condition is true for all the pairs of neighbors, the histogram has a zig-zag pattern. Otherwise, it does not have a zig-zag pattern. Figure 8 shows an example of this case. The minimum frequency restriction is required because not only do spherical shapes have a zag-zig chain code histogram, some regular symmetric shapes may also have the zig-zag pattern. In order to investigate this problem further, several simulated regular shapes were studied. Regular polygons with sides from 3 to 9 were digitized. The frequencies of chain codes for some regular shapes are presented in Table 1. The results showed that among the regular polygons with less than 8 sides, all of those with an even number of sides tend to have a zig-zag chain code histogram. Thus, rectangular and hexagonal shapes also have that pattern as shown in Figure 12. However, from Table 1, it can be noted that the frequencies for some direction codes were very low because they have less than 8 sides. Thus, these symmetric shapes can be separated from spherical shapes by their very low frequencies for at least some of the direction codes. TS AND DISCUSS A total of 136 airborne particles were analyzed following the procedure shown in Figure 13. Among them 16 were spherical particles and the rest were nonspherical particles. Each of them were well described in terms of whether or not it was a spherical particle. The program to perform this analysis was written in C for a SUN SPARCstation 2. ased on the preprocessed images, it took less than 2 min to finish the chain code histogram run for 136 particles. The output provided the shape information as to whether or not each was a spherical particle. Some simulated regular shapes were Hexagon. Rectangular 0.0 I I I I I I I Chain Code 12. Thc chain code histogram for rectangular and regular hexagonal shapes.

9 Use of Chain Code Histogram Method I I I I I I Image Nonagon n Octagon Thresholding ii X k I I I I I I Chain Code Chain Code Histo FIGURE 14. The chain code histogram of octagonal and nonagonal shapes. 0 Spherical? FIGURE 13. The flow chart for the whole procedure. also studied. The results showed that all the regular polygons with more than 7 sides tend to have very similar chain code histograms as that of spherical particles. Figure 14 shows the chain code histogram of both octagonal and nonagonal shapes. The reason for the inability to distinguish spherical shapes from octagonal shapes is that the resolution of this method was limited by the 8 directions. However, there are usually very few airborne particles with regular polygon shapes, and thus, this problem is not a serious one for the airborne particle studies. The possibility that this method can be incorporated into the on-line CCSEM system lies in the fact that when CCSEM system scans a filter, it can find the edge the secondary electrons. Thus, there is no need to do the preprocessing part. When the edge is detected, the relative position of the edge points can be stored. Thus, the chain code histogram can be easily obtained during the on-line scanning. Thcrcforc, this algorithm can be easily incorporated into the on-line system. In summary, this study showed that the chain code histogram method is a practical and quick way to calculate a shape index. Also, this study indicated that it would be possible to add such a feature to the on-line system of CCSEM so that this system may automatically analyze the individual particles and provide not only the chemical compositions but also the shape index in close to real time. This work has been supported by the National Science Foundation under grants ATM and ATM REFERENCES Casuccio, G. S., et al. (1983). J. Air Pollut. Control Assoc. 33: of the particle by the intensity contrast of Freeman, H. (1974). ACM Computing Suroeys

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