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We present a fully automatic method to detect doctored digital images. Our method is based on a rigorous consistency checking principle of physical characteristics among different arbitrarily shaped image regions. In this paper, we specifically study the camera response function (CRF), a fundamental property in cameras mapping input irradiance to output image intensity. A test image is first automatically segmented into distinct arbitrarily shaped regions. One CRF is estimated from each region using geometric invariants from locally planar irradiance points (LPIPs). To classify a boundary segment between two regions as authentic or spliced, CRF-based cross fitting and local image features are computed and fed to statistical classifiers. Such segment level scores are further fused to infer the image level authenticity. Tests on two data sets reach performance levels of 70% precision and 70% recall, showing promising potential for real-world applications. Moreover, we examine individual features and discover the key factor in splicing detection. Our experiments show that the anomaly introduced around splicing boundaries plays the major role in detecting splicing. Such finding is important for designing effective and efficient solutions to image splicing detection.