Acoustic sensors play an important role in autonomous underwater vehicles (AUVs). Sidescan sonar (SSS) detects a wide range and provides photo-realistic images in high resolution. However, SSS projects the 3D seafloor to 2D images, which are distorted by the AUV's altitude, target's range and sensor's resolution. As a result, the same physical area can show significant visual differences in SSS images from different survey lines, causing difficulties in tasks such as pixel correspondence and template matching. In this paper, a canonical transformation method consisting of intensity correction and slant range correction is proposed to decrease the above distortion. The intensity correction includes beam pattern correction and incident angle correction using three different Lambertian laws (cos, cos2, cot), whereas the slant range correction removes the nadir zone and projects the position of SSS elements into equally horizontally spaced, view-point independent bins. The proposed method is evaluated on real data collected by a HUGIN AUV, with manually-annotated pixel correspondence as ground truth reference. Experimental results on patch pairs compare similarity measures and keypoint descriptor matching. The results show that the canonical transformation can improve the patch similarity, as well as SIFT descriptor matching accuracy in different images where the same physical area was ensonified.

Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian. Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space. Since the canonical transformation preserves the Hamiltonian evolution, the model captures nonlinear collective modes in the learned latent representation. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model. The variational free energy calculation is based on the analytical form of physical Hamiltonian. While the phase space density estimation only requires samples in the coordinate space for separable Hamiltonians. We demonstrate appealing features of neural canonical transformation using toy problems including two-dimensional ring potential and harmonic chain. Finally, we apply the approach to real-world problems such as identifying slow collective modes in alanine dipeptide and conceptual compression of the MNIST dataset.