automatic estimation of direction of propagation of fire ...

AUTOMATIC ESTIMATION OF DIRECTION OF PROPAGATION OF FIRE FROM AERIAL IMAGERY Anthony Vodacek, Ambrose E. Ononye, Zhen Wang and Ying Li Center for Imaging Science, Rochester Institute of Technology Rochester, NY 14623, USA ABSTRACT BEHAVE and FARSITE are tools being used to predict the dynamic propagation of wildland fire based on a set of input parameters that must be known a priori. Their use is limited when the fire scene parameters are not immediately known. The research that led to the BEHAVE model has shown that the contour of a fire front is elliptic when viewed from a remote platform. By exploiting this shape property and employing the tools developed from differential geometry and image processing, we suggest a method for estimating direction and relative speed of fire fronts based solely on a single 2D remote image. This technique may be useful to quickly generate a fire map dynamics for dissemination to fire managers in situations where continual aerial monitoring is not possible. Results for this approach using AVIRIS data sets are presented.

1. INTRODUCTION The wildland is being destroyed by fire. Some of the fire incidents are triggered by lightning which sometimes go on undetected for days. Fire managers who respond to fire outbreak will need intelligent information regarding the state of the fire such as location, direction and speed of propagation. Their ability to effectively suppress the spread of fire will be incapacitated when these essential information are not available. A minute-by-minute progression of fire intelligence will be quite ideal but is not feasible as this will require minute-by-minute aerial monitoring. Predictions regarding the fire dynamics based on a set of input parameters will not be accurate as all the parameters needed for such prediction will not be time constant. Nevertheless, empirical predictions which yield good results are being used today. Some models have been proposed for making such predictions. Rothermel (Rothermel, 1983) described procedures for predicting fire behavior. His model is parametric and assumes that fine fuels transport the fire and produce flames at the fire front. Efforts towards creating a reliable and efficient model has led to semi-empirical based BEHAVE and FARSITE systems. The BEHAVE system which consists of FUEL and BURN subsytems is used to model fuel (FUEL) and predict fire behavior (BURN). The FUEL subsystem is discussed in (Burgan and Rothermel, 1984) while the BURN subsytem is described in (Andrews, 1986). The Fire Area Simulator (FARSITE) model uses BEHAVE to simulate spatial and temporal fire spread and behavior under the conditions of heterogeneous terrain, fuels and weather. These models might perform well below par if all the necessary input parameters are not known a priori. This makes their use to be impracticable for regions where terrain and local weather information are not immediately known. However, the research which led to the BEHAVE model has shown that the contour of propagating fire front from a point source is elliptic when viewed from a remote platform (Rothermel, 1983). Rothermel has also shown with Anderson’s equations (Anderson, 1983) for predicting fire shapes as function of effective windspeed, that this shape property is fairly well preserved. Wildland fires triggered by lightning can be regarded as point ignition type of fire and hence the scenario is consistent with elliptic shape.

We hereby propose a technique which is non-parametric but exploits the shape property mentioned above and in addition employs tools developed from differential geometry and image processing to automatically estimate direction of propagation and relative speed of fire fronts based solely on a single 2D remote image. This technique will be extremely valuable in situations where continual aerial montoring is not possible and also where fire map dynamics is to be generated quickly for immediate dissemination to fire managers. We will start with a quick overview of the essential mathematics and image processing tools needed.

2. DIFFERENTIAL GEOMETRY OF LEVEL SETS ~ is implicitly defined as: The level-set of a grayscale image is a curve in a plane. A plane curve, C ¾ ½µ ¶¯ x ¯¯ ~ = I(x, y) = 0 C y ¯

(1)

The orientation of this curve is given by its normal, ~n, ~n = =

∇I k∇Ik µ ¶ 1 Ix q Iy Ix2 + Iy2

and tangent, ~t is given by ~t = q 1 Ix2 + Iy2

µ

−Iy Ix

(2) (3)

¶ (4)

where Ix = ∂I(x,y) and Iy = ∂I(x,y) ∂x ∂y . We will need to derive an expression for the curvature, κ which is a measure of departure of curve from being a straight line. As illustrated in the figure 1 below (and is fully illustrated in (Thorpe, 1979)), κ defines three distinct regions.

Figure 1. The curvature

  < 0 =⇒ curve bends away from normal = 0 =⇒ curve is planar κ=  > 0 =⇒ curve bends towards normal The curvature is obtained by taking the derivative of the tangent along the tangent direction. Hence, κ = ∇~t · ~t

(5)

To derive an expression for κ let us define tx

=

ty

=

−Iy k∇I(x, y)k Ix k∇I(x, y)k

(6) (7)

=⇒ ∇tx

=

∇tx · ~t = =

µ ¶ 1 Ixx Ix Iy − Ixy Ix2 Ixy Ix Iy − Iyy Iy2 k∇I(x, y)k3 ¢ ¡ 1 2 2 2 ¡ ¢2 2Iy Ix Ixy − Iy Ix Ixx − Ix Iy Iyy Ix2 + Iy2 ¡ ¢ Ix 2 2 ¡ ¢2 2Ix Iy Ixy − Iy Ixx − Iy Iyy Ix2 + Iy2

Similarly, ∇ty · ~t = ¡

Iy Ix2 + Iy2

¡ ¢ 2 2 ¢2 2Ix Iy Ixy − Iy Ixx − Ix Iyy

(8)

(9)

(10)

Therefore, κ

=⇒ κ

=

∇~t · ~t

=

¡ ¢ ¡ ¢ ∇tx · ~t nx + ∇ty · ~t ny

=

Iy2 Ixx + Ix2 Iyy − 2Ix Iy Ixy ¡ ¢3/2 Ix2 + Iy2

=

Iy2 Ixx + Ix2 Iyy − 2Ix Iy Ixy k∇I(x, y)k3

(11)

2.1. Speed of Fire Front The speed of each fire pixel on propagating fire front is always directed along the normal to the front at that pixel location. The curve speed which is equivalent to the speed of fire front is defined as the time rate of change of the curve segment. The curve in an image is not an explicit function of time but rather has some embedded time information. The curve speed is therefore proportional to the magnitude of gradient. Hence, the gradient magnitude, k∇I(x, y)k of fire pixel at (x, y) is the measure of the speed of that fire pixel on the given propagating fire front. Detailed information on differential geometry of plane curves may be found in (Carmo, 1976; Thorpe, 1979; Gary, 1993).

3. PROCEDURE The procedure requires an application or implementation of the mathematical tools derived in the previous section along with the image processing tools. Caution has to be exercised in the choice of a suitable band for hyperspectral/multispectral imagery.

3.1. Band Selection Problem For the mathematical treatise discussed above to be applied to an image, curves in the given image must be identified. This means we need to construct an edge map (gradient image) and use a suitable threshold to identify the fire pixels. Sobel operators were used to generate gradient image. The resulting gradient image was then post-processed by an edge linking technique to fill in broken edges in the edge map subject to the criteria discussed in (Gonzalez and Woods, 2002). For hyperspectral or multispectral imagery, band choice is a very critical issue. We discussed the band selection problem in (Ononye et al., 2004). As discussed in the paper, a band which exhibits thermal saturation as shown

in figure 2, is to be avoided. This is because it would be difficult to construct a good edge map with such band. The saturation problem can be avoided by taking advantage of atmospheric attenuation in the choice of bands. For the AVIRIS imagery, the image created by taking average of bands 108 - 115 and 153 - 160 were used. This has an advantage over a single band as it has the tendency to reduce the noise level. These average images are shown in figure 3 along with band 218 which is saturated. The spectral profile of the fire area shown in the red rectangle is also illustrated in the figure. The automatic method of deducing threshold for post-processing the gradient image was discussed in (Ononye et al., 2004).

Figure 2. Band 107 AVIRIS Image and Spectral Profile

3.2. Dominant Fire Pixels The dominant fire pixels based solely on gradient magnitude were computed. To obtain dominant propagating fire pixels, the gradient magnitude of all the fire pixels were ordered from greatest to least. The pixel with the greatest gradient magnitude was deemed the dominant one. The next dominant one became the pixel with next highest gradient magnitude and so on. For high resolution image, this method of selecting dominant fire pixels and of course, the dominant fire fronts could result to a very tight cluster of about six to eight fire pixels about a common point on a fire front. Such situation will not convey any useful information especially if the aim is to find the first four or less dominant fire fronts. To ensure that other fire fronts were also considered, the location of the dominant fire pixel was deduced and all other fire pixels within the neighborhood of about 8 × 8 pixels window were excluded from the subsequent dominant fire pixel determination.

Figure 3. Spectral Profile of a fire area in a rectangle in (a) and average images of subimages of bands 108-114 and 154-160

3.3. Direction of Propagation of Dominant Fire Fronts The FARSITE model is in part an implementation of Huygens principle for propagating wave. The direction of propagation of fire pixels on fire front is directed along the normal vector and is consistent with the curvature, κ < 0 condition discussed in section two. Hence, in determining the dominant fire pixels, only those ones that satisfy this condition were used in the gradient ordering. Once the dominant fire pixel is found, its direction of propagation would lie along the normal vector at the pixel position. The influence of image noise could drastically affect the fire front direction deduced from a single normal vector. This problem could be avoided by using an aggregate of a four connected fire pixels around the dominant one.

4. RESULTS We tested our proposal with AVIRIS data sets of 1995 Cuiaba, Brazil fire. Figure 4 shows a subimage of band 107 of AVIRIS imagery over Cuiaba fire. In this figure, the gradient components Ix and Iy and gradient magnitude, k∇Ik are shown in (b), (c) and (d) respectively. These are gradients computed using Sobel operators. The post-processed gradient magnitude, in which the broken edges have been filled is shown in (e). This image demonstrates the fact that the fire fronts constitute the required 2D curves. Apart from the higher order spatial derivatives of image (Ixx , Ixy and Ixy ) not shown, the figure also shows images used to compute the curvature, κ, speed, dominant fire pixels and thresholds discussed in (Ononye et al., 2004) and direction of propagation of dominant fire pixels. The location of the dominant fire pixels are shown in Figure 5. In this figure, the post-processed image was used to generate thinned image shown in (b). The thinned image represents the 2D curve in image which is

the propagating fire front. The dominant fire pixels shown as dots are illustrated in (c). These results were integrated together by superimposing (c) on (b) to create dominant pixels on propagating fire fronts shown in (d). In figure 6, the directions of propagation of dominant fire pixels are illustrated. Each arrow in (e) shows the direction of a four connected fire pixels around each dominant one. The dots show the location of the dominant pixels. The input image (a), is the average of the subimage of bands 154 through 160. The gradient image and its post-processed version as well as the gradient skeleton are also shown. Figure 7 shows the results with full-size image, average of bands 154-160. The figure shows that the technique does not only work on subimage but also on full-size images.

5. CONCLUSION We have developed a useful tool that automatically estimates the locations and directions of propagation of dominant fire pixels on fire fronts. For a geo-rectified image, these locations could be related to the spatial coordinates. The tool is non-parametric but the user has control over the number of dominant fire pixels to be found. All other parameters like the threshold were automatically deduced from the image histogram. The technique uses only a single 2D remote image along with tools developed from differential geometry to generate the fire dynamics which could be quickly disseminated to the ground fire managers. It is particularly useful where continual aerial monitoring of fire is not possible and also in fire scenes that are completely covered by smoke. Work on this technique is not by any means deemed finished. Efforts are under way to test the algorithm with variety of imagery of known ground truth. In its finished form, it would generate a list or table of dominant fire fronts in an ordered form showing

• spatial coordinates of the dominant fire pixels • direction of propagation of fire pixels

Figure 4. Gradient images of subimage of band 107

Figure 5. Detected seven dominant fire pixels shown by dots

Figure 6. Direction of propagation of dominant fire pixels using average of bands 154-160 subimages

Figure 7. Results with a full-size image of average of bands 154-160

Acknowledgements This work was sponsored by NASA Grant NAG5-10051. The authors are grateful to Dr. Robert Kremens for providing some useful reference materials.

References Anderson, H. E. (1983). Predicting Wind-Driven Wildland Fire Size and Shape. USDA Forest Service Res. Pap.INT-305. Andrews, P. L. (January, 1986). BEHAVE: Fire Behavior Prediction and Fuel Modeling System – BURN Subsystem, Part 1. USDA Forest Service General Technical Report, NFES 0276. Burgan, R. E. and Rothermel, R. C. (June, 1984). BEHAVE: Fire Behavior Prediction and Fuel Modeling System . USDA Forest Service General Technical Report, INT -167. Carmo, M. P. (1976). Differential Geometry of Curves and Surfaces. Prentice-Hall. Gary, A. (1993). Modern Differential Geometry of Curves and Surfaces. CRC Press. Gonzalez, R. and Woods, R. (2002). Digital Image Processing. Addison-Wesley, second edition edition. Ononye, A., Vodacek, A., Wang, Z., and Li, Y. (April 2004). Mapping of Active Fire Area by Image Gradient Techniques. 10th Biennial Forest Service Remote Sensing Applications Conference, (In press). Rothermel, R. C. (June, 1983). How to Predict the Spread and Intensity of Forest and Range Fires. USDA Forest Service General Technical Report, NFES 1573. Thorpe, J. A. (1979). Elementary Topics in Differential Geometry. Springer-Verlag.