Edges characterize the boundaries of objects in images and are informative structural cues for computer vision and target/object detection and recognition systems. The Canny edge detector is widely regarded as the edge detection standard. It is fairly adaptable to different environments, as its parametric nature attempts to tailor the detection of edges based on image-dependent characteristics or the particular requirements of a given implementation. Though it has been used in a myriad of image processing tasks, the Canny edge detector is still vulnerable to edge losses, localization errors, and noise sensitivity. These issues are largely due to the key tradeoff made in the scale and size of the edge detection filters used by the algorithm. Small-scaled filters are sensitive to edges but also to noise, whereas large-scaled filters are robust to noise but could filter out fine details. In this paper, novel edge detection kernel generalizations and a shape-dependent edge detector are introduced to alleviate these shortcomings. While most standard edge detection algorithms are based on convolving the input image with fixed size square kernels, this paper will illustrate the benefits of different filter sizes, and more importantly, different kernel shapes for edge detection. Moreover, new edge fusion methods are introduced to more effectively combine the individual edge responses. Existing edge detectors, including the Canny edge detector, can be obtained from the generalized edge detector by specifying corresponding parameters and kernel shapes. The proposed representations and edge detector have been qualitatively and quantitatively evaluated on several different types of image data. Computer simulations demonstrate that nonsquare kernel approaches can outperform square kernel approaches such as Canny, Sobel, Prewitt, Roberts, and others, providing better tradeoffs between noise rejection, accurate edge localization, and resolution.