Image segmentation is important in improving the diagnostic capability of ultrasound computed tomography (USCT) and photoacoustic computed tomography (PACT), as it can be included in the image reconstruction process to improve image quality and quantification abilities. Segmenting the imaged object out of the background using image domain methods is easily complicated by low contrast, noise, and artifacts in the reconstructed image. Here, we introduce a new signal domain object segmentation method for USCT and PACT which does not require image reconstruction beforehand and is automatic, robust, computationally efficient, accurate, and straightforward. We first establish the relationship between the time-of-flight of the received first arrival waves and the object's boundary which is described by ellipse equations. Then, we show that the ellipses are tangent to the boundary. By looking for tangent points on the common tangent of neighboring ellipses, the boundary can be approximated with high fidelity. Imaging experiments of human fingers and mice cross-sections showed that our method provided equivalent or better segmentations than the optimal ones by active contours. In summary, our method greatly reduces the overall complexity of object segmentation and shows great potential in eliminating user dependency without sacrificing segmentation accuracy. The method can be further seamlessly incorporated into algorithms for other processing purposes in USCT and PACT, such as high-quality image reconstruction.