Additive Manufacturing (AM) is changing the manufacturing paradigm as it makes it possible to generate complex geometries that are impossible using conventional technologies. However, conventional GPS/GD&T practices are inadequate both at specifying and verifying geometric tolerances. In both cases, they lack the required flexibility. Applying volumetric instead of surface representations helps to solve the problem of specifying tolerances and coheres with topological optimization. The verification paradigm must be modified, too, as AM allows an increase in part complexity without a corresponding increase of cost. Among measurement techniques, only X-ray computed tomography (XCT), which is volumetric, is capable of easily measure complex parts. Leaving the discussion of volumetric tolerance specifications to the future, the aim of this work is exploring a part geometric accuracy verification by direct comparison between its nominal geometry and geometric tolerance volumetric representation, and an XCT volumetric image of it. Unlike the conventional use of XCT for geometric verification, this is a segmentation-free verification. The method is based on the “mutual information” of the two, i.e. information shared by the measured and nominal representations. The output is a conformance statement that does rely on a measurement but nor on a specific measured value not rely on a measurement result. This makes defining a decision rule considering consumer's and producer's risks difficult: uncertainty does not exist in this case. Statistic and simulation techniques make it possible to estimate these risks, defining a numerical model of the distribution of the gray values in a specific portion of the XCT image. Finally, an additive manufacturing case study validates the methodology.

增材制造（AM）改变了制造范式，因为它可以生成使用常规技术无法实现的复杂几何形状。但是，常规的GPS / GD＆T做法在指定和验证几何公差方面都是不够的。在这两种情况下，它们都缺乏所需的灵活性。应用体积代替表面表示有助于解决指定公差的问题，并与拓扑优化紧密结合。验证范式也必须修改，因为AM允许增加零件的复杂性而不会相应增加成本。在测量技术中，只有体积的X射线计算机断层扫描（XCT）能够轻松测量复杂的零件。不再讨论未来的体积公差规格，这项工作的目的是通过直接比较零件的名义几何尺寸和几何公差体积表示以及其XCT体积图像来探索零件的几何精度验证。与XCT用于几何验证的常规用法不同，这是无分段验证。该方法基于两者的“相互信息”，即由测量和名义表示共享的信息。输出是一个符合性声明，它不依赖于测量，但也不依赖于特定的测量值，不依赖于测量结果。这使定义考虑消费者和生产者风险的决策规则变得很困难：在这种情况下不存在不确定性。统计和模拟技术使估算这些风险成为可能，定义XCT图像特定部分中灰度值分布的数值模型。最后，增材制造案例研究验证了该方法。