<p>This study proposes a network that simultaneously performs (i) object detection (OD) and (ii) minimum depth estimation (MDE) from the camera to each object candidate. The proposed method processes stereo images captured in driving environments without relying on conventional stereo matching. The network, named ODMDENet, introduces novel techniques for jointly tackling OD and MDE, most notably a Slice-Wise Similarity Computation Module (SWSCM). From the left and right 3D feature maps generated by ODMDENet, SWSCM pools feature volumes corresponding to the bounding boxes of object candidates and divides them into an equal number of vertical slices along the width axis. It then computes similarities between each left slice and all right slices and linearly projects the resulting similarities to form a vector called Depth Feature Information (DFI). ODMDENet combines the DFI with object feature information from its OD module, forming a unified representation that enables improved performance in both OD and MDE. Due to the limited availability of suitable public datasets, we processed the KITTI and DrivingStereo datasets for training and evaluating ODMDENet. Experimental results demonstrate that the proposed method significantly outperforms existing approaches in both OD and MDE. The code is available at <a href="https://github.com/sjg918/kitti-slicedbread/">https://github.com/sjg918/kitti-slicedbread/</a></p>