A method implemented by one or more processors of a client device that facilitates touch-free interaction between one or more users and an automated assistant, the method comprising: receiving a stream of image frames that are based on output from one or more cameras of the client device; processing the image frames of the stream using at least one trained machine learning model (117A, 117B, 117C) stored locally on the client device to monitor for occurrence of both: an invocation gesture of a user captured by at least one of the image frames, and a gaze of the user that is directed toward the client device; wherein processing the image frames of the stream using at least one trained machine learning model stored locally on the client device to monitor for occurrence of both the invocation gesture and the gaze comprises: determining that a region of the image frames corresponds to an electronic display; and in response to determining that the region corresponds to the electronic display, ignoring the region in monitoring for the occurrence of both the invocation gesture and the gaze; detecting, based on the monitoring, occurrence of both: the invocation gesture, and the gaze; and in response to detecting the occurrence of both the invocation gesture and the gaze: causing at least one function of the automated assistant to be activated. receiving a stream of image frames that are based on output from one or more cameras of the client device; processing the image frames of the stream using at least one trained machine learning model (117A, 117B, 117C) stored locally on the client device to monitor for occurrence of both: an invocation gesture of a user captured by at least one of the image frames, and a gaze of the user that is directed toward the client device; wherein processing the image frames of the stream using at least one trained machine learning model stored locally on the client device to monitor for occurrence of both the invocation gesture and the gaze comprises: determining that a region of the image frames corresponds to an electronic display; and in response to determining that the region corresponds to the electronic display, ignoring the region in monitoring for the occurrence of both the invocation gesture and the gaze; an invocation gesture of a user captured by at least one of the image frames, and a gaze of the user that is directed toward the client device; wherein processing the image frames of the stream using at least one trained machine learning model stored locally on the client device to monitor for occurrence of both the invocation gesture and the gaze comprises: determining that a region of the image frames corresponds to an electronic display; and in response to determining that the region corresponds to the electronic display, ignoring the region in monitoring for the occurrence of both the invocation gesture and the gaze; determining that a region of the image frames corresponds to an electronic display; and in response to determining that the region corresponds to the electronic display, ignoring the region in monitoring for the occurrence of both the invocation gesture and the gaze; detecting, based on the monitoring, occurrence of both: the invocation gesture, and the gaze; and the invocation gesture, and the gaze; and in response to detecting the occurrence of both the invocation gesture and the gaze: causing at least one function of the automated assistant to be activated.