The transformed mean height profile (TMHP) technique, recently proposed in the context of interface analysis, smooths local fluctuations that give rise to intrinsic roughness in stochastic surfaces formed during nonequilibrium growth, by averaging the height field over bins of a specified size. In this work, we present an analytical proof that TMHP minimizes such intrinsic roughness, which in turn reduces spatial scaling corrections, thereby enabling more accurate characterization of both global and local roughness. Compared to recent existing methods, TMHP more effectively suppresses short-wavelength fluctuations while preserving intermediate- and long-wavelength features of the interface. We validate these findings using the ballistic deposition (BD) model on a substrate with dimension $d=2$, a case in which the consistent determination of the local roughness exponent had remained unresolved. By applying TMHP with an optimal bin size, we recover a local roughness exponent consistent with the most accurate numerical estimates of the global roughness exponent in the Kardar-Parisi-Zhang universality class for $d=2$, thereby resolving a longstanding gap in the scaling analysis of the BD model.

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• Ballistic deposition
• Growth processes
• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics
• Stochastic processes