Context. The matter distribution in the Universe exhibits a rich variety of structures, and they form the so-called cosmic web. These structures arise from the anisotropic gravitational collapse of primordial density fluctuations and define the pathways along which galaxies flow from low-density regions (voids) to the highest-density environments (galaxy clusters). The variation in local density across these structures plays a fundamental role in driving the environmental evolution of galaxies. Aims. To characterise the boundaries of filaments, we derived and analysed the galaxy overdensity profiles around filaments in two redshift ranges: 0.05 < z < 0.1 and 0.1 < z < 0.3. Methods. The profiles perpendicular and parallel to the filament directions were derived by averaging the galaxy overdensity as a function of distance. The characteristic scales and central overdensities of these profiles were then analysed by fitting several analytical models, grouped into two main families: exponential and power-law models. We also introduced normalised density profiles to analyse the impact of survey incompleteness. Results. The galaxy overdensity profiles in the perpendicular direction to filaments show an almost constant value in the central regions Dfila < 1 Mpc, with a decrease at larger distances until ≍10 Mpc. The mean physical widths of the filaments at redshifts 0.05 < z < 0.1 and 0.1 < z < 0.3, measured as the mean scale radii, are 2.39 ± 0.69 and 5.56 ± 2.29 Mpc, respectively. The difference in the scales in the two redshift ranges is also observed in the normalised density profiles. On the other hand, density profiles along filaments show a constant behaviour for distances larger than about 20 Mpc from the nearest intersection. Conclusions. The results presented in this work show that the zone of influence of cosmic filaments extends up to ∼10 Mpc from their spines. Moreover, a mild evolution in filament structural parameters is observed over the past ∼4 Gyr, suggesting that filaments undergo measurable changes even at relatively low redshifts.