Abstract: To better realize the great potential of amateur digital photography, the present invention introduces an intuitive system for digital manipulation. The system of the present invention allows a user to simply fix small blemishes in digital images. In one embodiment, the user merely places a cursor on the image blemish and activates a cursor control device such as a mouse button. In one embodiment, the blemish repair system is implemented using one of Dirichlet's theorems. The theorem provides a method of creating a smooth surface within a circle by using the values of points around the circle. To prevent the result from appearing too smooth, some pixelization may be added.

Abstract: To better realize the great potential of amateur digital photography, the present invention introduces an intuitive system for digital manipulation. The system of the present invention allows a user to simply fix small blemishes in digital images. In one embodiment, the user merely places a cursor on the image blemish and activates a cursor control device such as a mouse button. In one embodiment, the blemish repair system is implemented using one of Dirichlet's theorems. The theorem provides a method of creating a smooth surface within a circle by using the values of points around the circle. To prevent the result from appearing too smooth, some pixelization may be added.

Abstract: An improved exposure adjustment technique for brightening and darkening an image using a modified Gamma-like (G+) function is provided. The G+ function possesses characteristics such that, when applied brightening an image, the darker pixels are not enhanced too quickly when brightening, and the lighter pixels are not decreased too quickly when darkening. Two pertinent characteristics include the fact that the slope of the G+ function is not infinite at the origin, where “origin” corresponds to black pixels, and the slope near the origin, where corresponding to pixels are relatively dark, is lower than the slope of a conventional Gamma-like function.

Abstract: An improved sharpening technique sharpens an image using diffusion rather than a Gaussian blur in the smearing phase. After an appropriate radius or number of passes is determined for the pixels of an image, a diffusive process is applied to the image in the smearing phase to generate a blurred image. The values of each pixel in the original image are differenced with the values of each corresponding pixel in the blurred image. The difference may be weighted by input from a user. The resulting value is added to the original image and a sharpened version of the original image is created.

Abstract: Polyolefin product produced using process conducted in apparatus for olefin polymerization which includes one or more shell and tube olefin polymerization reactors, each of which has an olefin polymerization reaction mixture inlet connection and a crude polyolefin product outlet connection. Each reactor is equipped with a recirculation system including a pump arranged to circulate a reaction mixture through the tube side of the reactor independently of the introduction of olefin polymerization reaction mixture into the reactor. The apparatus may also include an inlet reaction mixture distribution manifold and an outlet polymerization reaction mixture collection manifold interconnecting the reactors for operation in parallel. The apparatus also includes catalyst composition and catalyst modifier inlets for each reactor arranged such that a catalyst modifier to may be introduced into each reactor at a rate which is independent of the introduction of catalyst composition.

Abstract: Apparatus for olefin polymerization includes one or more shell and tube olefin polymerization reactors, each of which has an olefin polymerization reaction mixture inlet connection and a crude polyolefin product outlet connection. Each reactor is equipped with a recirculation system including a pump arranged to circulate a reaction mixture through the tube side of the reactor independently of the introduction of olefin polymerization reaction mixture into the reactor. The apparatus may also include an inlet reaction mixture distribution manifold and an outlet polymerization reaction mixture collection manifold interconnecting the reactors for operation in parallel. The apparatus also includes catalyst composition and catalyst modifier inlets for each reactor arranged such that a catalyst modifier to may be introduced into each reactor at a rate which is independent of the introduction of catalyst composition.