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Objective: In clinical ultrasound, current 2-D strain imaging faces challenges in quantifying three orthogonal normal strain components. This requires separate image acquisitions based on the pixel-dependent cardiac coordinate system, leading to additional computations and estimation discrepancies due to probe orientation. Most systems lack shear strain information, as displaying all components is challenging to interpret. Methods: This paper presents a 3-D high-spatial-resolution, coordinate-independent strain imaging approach based on principal stretch and axis estimation. All strain components are transformed into three principal stretches along three normal principal axes, enabling direct visualization of the primary deformation. We devised an efficient 3-D speckle tracking method with tilt filtering, incorporating randomized searching in a two-pass tracking framework and rotating the phase of the 3-D correlation function for robust filtering. The proposed speckle tracking approach significantly improves estimates of displacement gradients related to the axial displacement component. Non-axial displacement gradient estimates are enhanced using a correlation-weighted least-squares method constrained by tissue incompressibility. Results: Simulated and in vivo canine cardiac datasets were evaluated to estimate Lagrangian strains from end-diastole to end-systole. The proposed speckle tracking method improves displacement estimation by a factor of 4.3 to 10.5 over conventional 1-pass processing. Maximum principal axis/direction imaging enables better detection of local disease regions than conventional strain imaging. Conclusion: Coordinate-independent tracking can identify myocardial abnormalities with high accuracy. Significance: This study offers enhanced accuracy and robustness in strain imaging compared to current methods.