This paper presents ATOM, an integrated framework towards agnostic and tangible object interactions with microgestures. Our goal is to support microgesture interactions across different everyday objects, with the capability to automatically leverage the geometric affordance of each object. We formulate a fingertip-aware detection pipeline to leverage generative 2D and 3D models for geometry enhancement and refinement. We then introduce a usability-based method to prioritize the detected elements based on their ergonomic suitability for interactions. Building on this foundation, we further develop an AR system to transform everyday handheld objects into tangible user interfaces with 0D, 1D, and 2D microgesture interactions. Across transitions among everyday cooking objects of varying shapes and sizes, ATOM outperformed ablation baselines in task completion, usability (SUS), and workload (NASA-TLX). A further study with 10 objects demonstrates ATOM's generalizability across objects and grasps, highlighting its potential towards fluid, object-agnostic tangible interaction in real-world AR scenarios.

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