X-ray photons which are scattered inside the object slice and reach the detector array increase the detected signal and produce image artifacts as "cupping" effects in large objects and dark bands between regions of high attenuation. The artifact amplitudes increase with scanned volume or slice width. Object scatter can be reduced in third generation computed tomography (CT) geometry by collimating the detector elements. However, a correction can still improve image quality. For fourth generation CT geometry, only poor anti-scatter collimation is possible and a numeric correction is necessary. This paper presents a correction algorithm which can be parameterized for third and fourth generation CT geometry. The method requires low computational effort and allows flexible application to different body regions by simple parameter adjustments. The object scatter intensity which is subtracted from the measured signal is calculated with convolution of the weighted and windowed projection data with a spatially invariant "scatter convolution function". The scatter convolution function is approximated for the desired scanner geometry from pencil beam simulations and measurements using coherent and incoherent differential scatter cross section data. Several examples of phantom and medical objects scanned with third and fourth generation CT systems are discussed. In third generation scanners, scatter artifacts are effectively corrected. For fourth generation geometry with poor anti-scatter collimation, object scatter artifacts are strongly reduced.