3D modeling of cultural heritage objects like artifacts, statues and buildings is nowadays an important tool for virtual museums, preservation and restoration. In this paper, we introduce a method to automatically design a minimal imaging network for the 3D modeling of cultural heritage objects. This becomes important for reducing the image capture time and processing when documenting large and complex sites. Moreover, such a minimal camera network design is desirable for imaging non-digitally documented artifacts in museums and other archeological sites to avoid disturbing the visitors for a long time and/or moving delicate precious objects to complete the documentation task. The developed method is tested on the Iraqi famous statue "Lamassu". Lamassu is a human-headed winged bull of over 4.25 m in height from the era of Ashurnasirpal II (883-859 BC). Close-range photogrammetry is used for the 3D modeling task where a dense ordered imaging network of 45 high resolution images were captured around Lamassu with an object sample distance of 1 mm. These images constitute a dense network and the aim of our study was to apply our method to reduce the number of images for the 3D modeling and at the same time preserve pre-defined point accuracy. Temporary control points were fixed evenly on the body of Lamassu and measured by using a total station for the external validation and scaling purpose. Two network filtering methods are implemented and three different software packages are used to investigate the efficiency of the image orientation and modeling of the statue in the filtered (reduced) image networks. Internal and external validation results prove that minimal image networks can provide highly accurate records and efficiency in terms of visualization, completeness, processing time (>60% reduction) and the final accuracy of 1 mm.