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In our series of studies on noninvasive assessment of the regional elasticity of the arterial wall, the displacement gradient (change in thickness) of the arterial wall caused by the heartbeat was measured by the phased tracking method. Because the displacement gradient corresponds to the strain due to the change in blood pressure, the elasticity can be evaluated from the displacement gradient of the arterial wall and the blood pressure, which are noninvasively measured at the upper arm. In the measurement of the elasticity of the arterial wall by our method, the region in which the elastic modulus is estimated must be assigned beforehand; currently, the lumen-intima boundary of the arterial wall is manually determined by the operator. For the real-time measurement of the elasticity of the arterial wall, a fast, automated method is necessary for detection of the boundary. In this paper, a cost function is proposed for differentiation of the arterial wall from the lumen. The proposed cost function was applied to ultrasound data, which were noninvasively obtained for five human carotid arteries. In comparison with the case of detection using only the amplitude of the echo, the root mean square error between the automatically detected lumen-intima boundary and the manually assigned boundary was significantly improved by using the proposed cost function. Furthermore, the lumen- intima boundary was automatically detected in a short period. Such a method is required for real-time measurement of the elasticity of the arterial wall, though detection of the outer boundary of the adventitia, which is not described in this paper, is also necessary to realize real-time elasticity measurement by our method.