STATISTICAL DETECTION OF SALIENT POINTS USING THE DUAL TREE M-BAND WAVELET TRANSFORM W. Ayadi 1,2 ,S. Sevestre-Ghalila 2,3 , A. Benazza-Benyahia 1 1 URISA, Ecole Sup´ erieure des Communications, Tunisia walid.ayadi@gmail.com benazza.amel@supcom.rnu.tn 2 MAP5, Universit´ e Paris 5, France 3 U2S, ENIT, Tunisia sylvie.sevestre@math-info.univ-paris5.fr ABSTRACT In this paper, we develop a novel method to detect salient points in an image from a multiresolution representation. Our contribution is twofold. Firstly, the multiscale rep- resentation results from the Dual Tree Wavelet Transform (DTWT) since it enables a great directional selectivity with a reduced redundancy ratio. The second novelty of our work relies on the reliable outliers statistical tests that we apply to detect salient points from the DTWT coefficients. The exper- iments show the robustness of the approach to noise. 1. INTRODUCTION During the past years, a great interest has been given to glob- ally describe any image by defining appropriate signatures built on its keypoints or Salient Points (SP). By SP, we mean pixels carrying enough information about the local neighbor- hood so that they will be distinct from their nearest neigh- bors. They are also characterized by their robustness to scal- ing, rotation and illumination changes. Their positions are invariant with respect to geometric and radiometric distor- tions [1]. Typical examples of SP are blobs, corners and junctions. SP detection is a key issue for various matching problems in computer vision such as image retrieval [2, 3], object recognition [4]. SP detectors can be classified in two categories. The first one employs contours [5]. However, this class of detectors is not always the most suitable one since edge extraction is very sensitive to noise and the con- tour chaining may not be well in cluttered scenes. In the sec- ond class of detectors, the Harris detector [6] is the most em- ployed technique. It consists in locating the local changes in the image by using the first derivative. This detector is robust to image rotation, additive noise and illumination changes but it is not designed for deriving SPs at different scales. Recently, it has been modified to work as a scale-invariant detector [7]. Another solution is to perform the SP detec- tion in a transform domain which is expected to make the problem easier to solve. To this respect, multiscale trans- forms are suited to this task since they decompose the input image into different scales and orientation that are coherent with the human perception. In [3], a multiresolution frame- work is retained to detect global as well local image vari- ations and the interest points are assumed to correspond to areas where the local contrast is the highest. However, the lack of shift invariance and the directional selectivity of the wavelet transform has motivated the choice of more sophis- ticated scale-space transforms [8]. In [9], the dual tree com- plex wavelet transform is used to generate an “accumulated energy map” that enables the keypoint selection. However, it is worth noting that heuristic criteria have been considered at the detection step. In this paper, we propose a novel mul- tiscale keypoint detection. Our approach departs from the conventional ones: instead of using empirical criteria, SP ex- traction is based on outliers statistical tests performed at dif- ferent scales. Furthermore, we will operate in the Dual Tree M-band Wavelet Transform (DTWT) since it has been recog- nized to offer a great directional selectivity and to be nearly shift invariant with a limited redundancy w.r.t. the dual tree complex wavelet transform [10]. The rest of this paper is organized as follows. Section 2 is dedicated to a review of DTWT. In section 3, we describe the statistical behavior of wavelet details coefficients. In Section 4, we briefly describe the most pertinent outliers statistical tests. Then, in Section 5, we explain how we apply them for detecting SP from the resulting DTWT coefficients. In Section 6, experimental re- sults are given and some conclusions are drawn in Section 7. 2. A BRIEF REVIEW OF M-BAND DTWT Multiresolution decomposition allows a multiscale analysis of the details contained in the image corresponding to phys- ical structures. An M-band wavelet transform of L 2 (R), (where M ∈ N ∗ ) is considered as a very versatile multi- scale decomposition. It is characterized by a scaling func- tion φ ∈ L 2 (R), and M − 1 wavelet functions ψ m ∈ L 2 (R), (m = 1,..., M − 1) that satisfy the following dilation equa- tions: ∀t ∈ R, φ (t )= √ M ∑ k∈Z h 0 (k)φ (Mt − k) (1) ψ m (t )= √ M ∑ k∈Z h m (k)φ (Mt − k), (2) where the h m ∈ ℓ 2 (Z). The set ∪ M−1 m=1 {M − j/2 ψ m (M − j t − k)} j,k∈Z is an orthonormal basis of L 2 (R) if the para-unitary condition holds for any couple (m, m ′ ) in {0,..., M − 1} 2 : M−1 ∑ p=0 ˆ h m (ω + p 2π M ) ˆ h ′ m (ω + p 2π M )= Mδ m−m ′ , (3) where ˆ · denotes the Fourier transform. Therefore, h 0 is a low-pass filter, h 1 ,..., h M−2 are band-pass filter and h M−1 is a high-pass filter. Consequently, the expansion of any 1D signal f ∈ L 2 (R) over J resolution levels can be expressed 16th European Signal Processing Conference (EUSIPCO 2008), Lausanne, Switzerland, August 25-29, 2008, copyright by EURASIP