A NEW SIGNATURE BASED ON RADON ...

Rθ-SIGNATURE: A NEW SIGNATURE BASED ON RADON TRANSFORM AND ITS APPLICATION IN BUILDINGS EXTRACTION Hmida Rojbani, Ines Elouedi and Atef Hamouda Laboratory of Computing in Programming, Algorithmic and Heuristic/Image, City and Environment, Faculty of Sciences of Tunis, Campus Universities - Tunis - 1060, Tunisia Email: [email protected], [email protected], atef [email protected]. ABSTRACT Object recognition has been a topic of research for decades, it operates by making decisions based on the values of several shape properties measured from an image of the object. In this paper, a new exploitation of the Radon Transform (RT) is proposed to extract only one projection according to a single angle. This projection is chosen in way that contains the necessary information to recognize an object (a shape descriptor). This descriptor (called Rθ-signature) provides global information of a binary shape regardless its form. After that, we use this signature in an extraction method of buildings from very high-resolution satellite imagery. Index Terms— Shape descriptor, Radon Transform, Rθsignature, Buildings extraction. 1. INTRODUCTION As the holy grail of computer vision research is to tell a story from a single image or a sequence of images, object recognition has been studied for more than four decades [1] [2]. We try here to recognize buildings in very high resolution satellite imagery. And that by comparing segments from the target image with building’s models. Also, we can divide the building extraction methods in four categories: • Approaches ”based images”, which exploit directly the information at the pixel level. [3] • Approaches ”based auxiliary data”, using other ”dataset” instead of satellite images (Digital Elevation Model ...). [4] • Approaches ”based 2D models”, which refer to a library of a priori two-dimensional models of buildings. [5] • Approaches ”mixed”, which combine two or more of the three categories mentioned above. [6] Our work subscribes under the third category ”based 2D models”, which we compare the segments of the images by

the models from library using a new descriptor based on the Radon transform (RT). To match the segment by the models they must be simplified, this simplified representation of is also called a shape descriptor or signature. This is an abstraction of a structured model that captures most of the important information of the form. These simplified representations are easier to handle, store and compare than the forms directly. Here in we tried to locate and extract a signature from the Radon space itself without any modification in the RT formula. Our work is motivated by the study introduced by Magli et al. in [7] twelve years ago, where they provide the existence of projection according to an angle from the Radon space contains the information can present the object. Actually our work is finding the method to locate this projection which we called the Rθ-signature. This paper is outlined as follows. After we recall the definition and the properties of the RT in sections 2, we present in Section 3 our Rθ-signature approach. Followed by the buildings extraction methods and experiments and discussion are given in Section 5. Finally we summarize our research and conclude the paper in Section 6. 2. THE RADON TRANSFORM By definition the Radon transform [8], of an image is determined by a set of projections of the image along lines taken at different angles. For discrete binary image data, each nonzero image point is projected into a Radon matrix. Let f(x,y) be an image. Its Radon transform is defined by [9]: ∫ +∞ ∫ +∞ TR f (ρ, θ) = f (x, y)δ(ρ−x cos θ−y sin θ)dxdy. −∞

−∞

(1) Where δ(.) is the Dirac function, θ ∈ [0, π] and ρ ∈] − ∞, +∞[. To represent the RT of an image, we take multiple, parallel-beam projections of the image from different angles by rotating the source around the center of the image. The Fig. shows a single projection at a specified rotation angle. The RT is robust to noise, provided with fast algorithms, and it projects a two-dimensional function into one-dimensional

Fig. 1. Parallel-Beam Projection at Rotation Angle Theta.(After [10])

Moreover, we can consider an object as a lot of parallel lines put one beside the other, which means that in the right angle projection, those lines will raise a lot of peaks in the Radon space. So if we calculate the sum of the Radon coefficients in this projection, this sum will be higher than the others. Based in this analyse, we sum the Radon values of ρ in each θ angle and we pick the angles with the higher sum. Apply on the object in Fig.2(a), we find that the projections shown in Fig.2(c) and Fig.2(d) satisfy this condition. Then a study on the distribution coefficients of Radon in each selected projection is made. We seek the maximum coefficient in each selected projection and calculate the division ratio of the projection p: DRp =

function, for all this reasons, we have decided to employ the RT. 3. THE Rθ-SIGNATURE In our study a new exploitation of the RT is proposed. Usually the RT used only in the detection of straight lines. In our work we provide global information of a full binary shape, whatever its form; scale and orientation are, by generating a new signature (Rθ-signature). We define this signature using the RT’s property proved by Magli et al. [7], which is the existence of a peak among the Radon projections, which exhibits the same shape of the projected object in the ρ direction. To find this projection (we called the Rθ-signature), Magli et al. use the wavelet transform. They calculate the similarity between the mother wavelet (look alike the projected object) and the peak in each Radon project. The projection with the highest degree of similarity selected as the represented projection of the object. The disadvantages of this approach are:

maximum coef f icient the sum of coef f icient

(2)

The DRp belongs to [0, 1], if the DRp is close to 1 then the weight of the sum is carried by the maximum element, this means that the data are concentrated in only one point which is the maximum coefficient of the projection. However, if the ratio is close to 0, the coefficients in the projection are well distributed which gives a cloud of peaks more significant. So, the projection with the DRp lowest is chosen as the ”Rθsignature”. In our example, since the projection Fig.2(c) satisfies the two conditions, it is the ”Rθ-signature” of the object in Fig.2(a). By generating our new signature (Rθ-signature),

• Several mother wavelet functions are used because the shape of the peak is generally unknown. • The setting of these wavelets is not trivial.

(a) input image

(b) the Radon Transform of the image

Here we present an approach that allows the extraction of the projection of a simpler and more efficient way. It can also work with an object of any shape. 3.1. The concept of the Rθ-signature We thought to seek the projection the most revealing form of projected object, i.e., the one that provides the most information about the object in question. This amount to look for the angle θ which gives the perfect projection, this projection is the ”Rθ-signature”. In the fact, since the RT is linear by definition, geometric properties like straight lines can be made explicitly by the RT which concentrates energies (loci of intersection of several sinusoidal curves), from the image in few high-valued coefficients in the transformed domain.

(c) the profile according to angle 6◦ (d) the profile according to angle 179◦

Fig. 2. the work flow to generate the Rθ-signature we provide global information of a binary shape, whatever its form is. One can wonder why a binary shape, in fact, the principal operation of the RT in the discrete way (image) is the summation of the intensity of pixels along the same line

for each projection. To obtain an outcome that reflects only the shape, the object must have a unique color. Otherwise the result of RT reflects the brightness of the object in addition to its shape. For that, we will use binary images to simplify the calculation. 3.2. Proprieties of Rθ-signature Our signature preserve the proprieties of the RT (rotation, translation and scaling in Fig.3(b), 3(d) and 3(f)) and that because the signature approach do not interfere in the calculation of the RT but in the way of reading the data of the Radon space. It thus has three essential properties for a good form descriptor. In addition, the signature proves to be an excellent shape measurement and it gives very good results with solid symbols (i.e. no contour or an empty symbol). Otherwise, we observe that the signature tends to compress the form so compress the signature (Fig.3(h))) and that refer to the less of information to sum when we use the contour only. One of the advantages of the proposed approach is its robustness to additive noise. This robustness is inherited from the RT itself. More details about the Rθ-signature exist in [11].

(a) original image rotate by 95◦

(b) the Rθ-signature (rotation)

(c) original image translated

(d) the Rθ-signature (translation)

4. BUILDINGS EXTRACTION USING Rθ-SIGNATURE In this section, we put the Rθ-signature under the investigation. And that by the extraction of building only from a Quickbird satellite image. Before we can use the signature a segmentation phase is needed to extract potential building. The Mean Shift segmentation is the applied algorithm. The approach consists of three steps to extract the buildings from high resolution satellite image: (i) segmenting the image using mean shift procedure; (ii) calculating the R?signature for every object found in step (i); (iii) matching the selected signature with a perfect building’s model, and getting the similarity percentage. The approach is illustrated in Fig.4.

(e) original image scaled by 3

(f) the Rθ-signature (scale)

(g) the contour of the original object

(h) the Rθ-signature

4.1. Image Segmentation The man-made objects generally have straight edges that cause straight forms in an image, although, in the present case, the predominant building shape is rectangular in the selected study area (Fig.5). Due to different ages and building materials, there is significant grey variability in some building regions. The grey deviation will cause poor segmentation results. There are some good approaches such as Gauss filter, and wavelet filter, to smooth the image, yet all of them have such shortcoming as blurring abrupt changes, i.e. building

Fig. 3. the proprieties of Rθ-signature

Fig. 4. The building extraction workflow

boundaries. But the Mean shift provide a discontinue preserving filtering which resolve this problem. The mean shift method presents an elegant way to locate these density maxima without having to estimate the density directly [12]. The mean shift vector always points to the direction of maximum increase in the density. The mean shift process is an iterative procedure that shifts each data point to these density maxima. After that we detect the edge of the original image by means the Canny method [13] and we superpose the edge map found over the filtered image. This proposed pre-treatment will guides the mean shift algorithm to find the mode within a local region in the resulted image more reasonably. Because the density maxima in the image are given now by the edge map which make mean shift segmentation guided by those edge. The result of the segmentation is shown in Fig.6, where each color refers to a segment (or object). After the mean shift segmentation phase, segments with sizes smaller than a building size threshold are removed.

Fig. 6. The Mean Shift segmentation result image. 4.2. Object Parameters Estimation using the Rθ-signature To test the validity of our signature approach, we used in the decisional phase, where we filter the segments created by the segmentation phase. We use the Rθ-signature described in section 3 to extract the feature of each extracted segment. we compute the Rθ-signature each object to matched this signature with the samples of buildings ( i.e the Rθ signature of perfect building). 4.3. Matching with a building model The Rθ-signature is a one-dimensional signal, so we can use the signal proprieties to calculate the similarity, between an object signature and a several models signatures of different size of buildings (we can suppose that Fig.2(d) is one of the models signatures). In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them [14]. A way to compute the similarity is to use maximum cross-correlation; the maximum value of cross-correlation takes care of the ρ-delay between signals. As far as correcting for amplitude goes, we normalize the signals so that their self-cross-correlation is 1.0, with respect to what threshold to use for acceptance/rejection, after some experience we chose 0.9 as threshold to accept an object. The same treatment is used for all other object and matching to the same building model profile. The result of the above algorithms is shown in Fig.7. 5. THE EXPERIMENTAL RESULTS

Fig. 5. QuickBird satellite image covering the city of Strasbourg in 2008.

The method developed in this study was applied to extract buildings from a Quickbird image with a spatial resolution is 0.6 meter/pixel. The results of extraction are compared with manually digitized reference data to conduct an accuracy assessment. The experimental results are very promising. In the

Table 2. Numerical Comparison Of The CDB [6], The DRV [3] And The Proposed Methods (Rθ). Reference Buildings not detected False buildings alarms CDB DRV Rθ CDB DRV Rθ 510 30 47 60 53 30 19 ALL(%∗ ) 6 10 11 10 6 4 ∗ the missing/false objects are given in percent of all building

Fig. 7. The final building extraction qualitative analysis the objective was to determine the practicability of the proposed approach whereby a building extracted percentage rate is calculated. We use a metric proposed in [15] : BER =

BCE ∗ 100. (BCE + BP E + BN E)

(3)

Where BER is the building extraction rate, BCE is the building correctly extracted, BPE is the number of buildings partially extracted and BNE is number of buildings not extracted. Table 1 presents the extraction rate in each test area (TA).

Table 1. Building Extraction Results TA1 TA2 TA3 TA4 TA5 Final Results BCE 91 158 72 66 40 427 BPE 5 11 4 4 1 23 BNE 14 32 6 8 5 60 Extraction 82 78 87 84 85 83 Rate (%)

The average of the extraction rate is 83%. In [16], the authors define an approach based on RT to extract contour od building taken from a high-resolution satellite image . This approach suffers of many obstacles, such as the dependance relation between the build size to extract, and the frostner operator to choose. Also probably it will fail to extract the buildings contours in a large image contains numerous buildings, for that each building must treated separately. For comparison, we have selected four methodologically different reference techniques from the literature :

a Change Detection of Buildings (CDB) method [6] and an approach base on DRV (DRV) [3]. We have taken care of choosing references which use similar image features to our framework, but they exploit them in different manners. More precisely, in CDB [6], the authors based there work on prior knowledge existing in geodatabase, this methodology is composed of several stages. The existing knowledge on the buildings and the other urban objects are first modeled and saved in a knowledge base. Some change detection rules are defined at this stage. Then, the image is segmented. The parameters of segmentation are computed thanks to the integration between the image and the geodatabase. Thereafter, the segmented image is analyzed using the knowledge base to localize the segments where the change of building is likely to occur. The change detection rules are then applied on these segments to identify the segments that represent the changes of buildings. These changes represent the updates of buildings to be added to the geodatabase. On the other hand, the DRV [3] is based on a variance ratio, called DRV. This means the exploitation of the variance parameter, which corresponds to the sum of deviations of each of the pixels in windows of varying size with the average value of these pixels. The DRV is defined as the ratio between the variance of the contour and body building, which permits discrimination against its environment. Indeed, in the presence of a building as the size of the window, the variance of the body is low (doing its homogeneity), while the variance of the edge is sharp, since it describes the transition between two levels gray. DRV values corresponding to this calculation is then maximum. The values of DRV to be above a threshold set arbitrarily will be accepted. In table 2 and Fig.8 , a comparison results with the three method ( CDB, DRV and our proposed approach Rθ) are given. In the quantitative evaluation we counted the number of missing and falsely detected objects. The results shown in Table 2 and Fig.8, prove that, despite the two other method are semi-automatic method, our automatic method gives good results. 6. CONCLUSION In this work we have presented a new approach to characterizing an object using the Radon transform. This approach extracts invariant features from Radon projection of an image obtained after a pre-processing phase in which a profile ac-

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Fig. 8. The comparison results of the three methods

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