Shake-the-Box (STB) has become the de facto standard Lagrangian Particle Tracking (LPT) approach that reconstructs the 3D particle tracks from time-resolved particle-seeded stereoscopic images. STB is the only available LPT method on the market that works on highly concentrated particle images. Many developments on the STB method have been published ever since. But very few works exist to improve the core tracking ability of STB. We argue that STB's optimization scheme can be less effective or even fail with sparse temporal data or with data extracted from complex flows. The consequences are either one track is terminated prematurely, or one particle is identified on the wrong track. The main reason is that STB's optimization scheme requires the cost function to be relatively smooth locally to perform well. In this work, we propose a tracking scheme rooted in the function learning/approximation paradigm. Our approach is based on kernel methods and is thus called Kernelized LPT (KLPT). KLPT is evaluated against both synthetic and real experiments and produces accurate results for data with medium to high ppp levels and large time separation. We also apply KLPT to real experimental data depicting an impinging jet at Re=2500. We observe that, compared to STB (Davis 10), KLPT can capture longer tracks and allows more detailed flow reconstruction in highly turbulent regions. We conclude that our KLPT scheme is always more robust than STB and more accurate for densely seeded particle flow fields. Another work line is to retrieve the volumetric velocity filed on Eulerian grids from the Lagrangian data generated by STB. We argue that if only the Eulerian flow variables are needed, it is naturally more accurate to base our knowledge on raw images instead of passing through the redundant LPT procedure. Our proposed method Lagrangian PIV (LaPIV), infers the volumetric velocity fields from raw image data without any intermediate procedure. To this end, we adopt the above kernel formulation under KLPT, taking account of a transport model that links the particles’ 3D coordinate X at frame k to the Eulerian velocity field at frame k-1. By doing so, we can obtain the unknown flow velocity field. Our formulation allows estimating the velocity vector through tracking a group of particles, contrary to single-particle tracking done in KLPT.