Bi-level iso-surface compression

An encoding method comprising:

• determining values of occupancy bits of an occupancy image as a function of a 3D regular grid, a scalar function and an isolevel, the occupancy image embodied in computer-readable material for use in at least one of a computer graphics application and a scientific visualization application to represent isosurface data in compressed form, and having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism, the method further comprising:
• visiting the nodes of the three-dimensional grid in a scanning order,
• visiting the nodes of the three-dimensional grid in a scanning order,
• comparing the function value associated with each node with the isolevel,
• setting a value of the occupancy bit associated with each node to a first value if the function value is less than the isolevel,
• setting the value of the occupancy bit associated with each node to a second value if the function value is higher than the isolevel, and
• employing the occupancy bit value associated with each node in said occupancy image embodied in said computer-readable material for use in said at least one of said computer graphics application and said scientific visualization application to represent isosurface data in compressed form.

A decoding method comprising reconstructing an isosurface polygon mesh from an occupancy image, comprising the steps of:

• taking compressed surface data as input and producing surface data as output, said mesh having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism;
• reconstructing the occupancy image by decoding an occupancy image record;
• determining intersection edges and decoding intersection points and corresponding normal vectors from an intersection points record and an normal vectors record, respectively, if present in the compressed isosurface data;
• assigning default values to the intersection points and corresponding normal vectors, if the intersection points record and normal vectors record are not present in the compressed isosurface data, and
• employing results of the steps of reconstructing, determining and assigning in said occupancy image embodied in a computer-readable material for use in at least one of a computer graphics application and a scientific visualization application to represent the isosurface data.

A method comprising an in-core isosurface decoder process embodied in computer-readable material producing a polygon mesh as a surface representation, said mesh having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism, the process including:

• taking as input compressed isosurface data without an optional intersection points record and without a normal vectors record;
• setting normalized intersection points to a default value of one half,
• giving normal vectors default values being a function of neighboring intersection point values;
• using a smoothing algorithm as a global predictor to form and improve a quality of a reconstructed polygon mesh, and
• employing results of the steps of setting, giving and using in producing said polygon mesh as said surface representation, embodied in said computer-readable material for use in at least one of a computer graphics application and a scientific visualization application.

A method comprising an out-of-core isosurface decoder process producing a set of oriented points as a surface representation, the process including:

• taking as input compressed isosurface data with any optional intersection points record and any optional normal vectors record;
• generating one oriented point after decoding and reconstructing each said any optional intersection point and corresponding said any optional normal vector, and
• employing results of the steps of taking and generating in producing said set of oriented points as said surface representation, embodied in a computer-readable material for use in at least one of a computer graphics application and a scientific visualization application;
• and reconstructing an isosurface polygon mesh from said set of oriented points as a surface representation, said mesh having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism.

A system comprising:

• a memory of a computer system storing the data structure for representing an isosurface polygonal mesh and having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism, the isosurface polygonal mesh approximating a level set of a scalar function, the scalar function defined by function values and a regular three-dimensional grid, the level set defined by an isolevel, each function value associated with a node of the regular three-dimensional grid, the data structure having an occupancy record, the occupancy record including a three-dimensional occupancy image, the three-dimensional occupancy image composed of occupancy bits, each occupancy bit associated with a node of the three-dimensional grid, each occupancy bit being equal to either a first value or a second value, each occupancy bit having a corresponding function value, each occupancy bit being equal to the first value if the corresponding function value is less than the isolevel, and to the second value if the corresponding function value is higher than the isolevel.

A method comprising:

• storing a data structure for representing an isosurface polygonal mesh, and having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism, the isosurface polygonal mesh approximating a level set of a scalar function, the scalar function defined by function values and a regular three-dimensional grid, the level set defined by an isolevel, each function value associated with a node of the regular three-dimensional grid,
• providing the data structure with an occupancy record, the occupancy record including a three-dimensional occupancy image, the three-dimensional occupancy image composed of occupancy bits, each occupancy bit associated with a node of the three-dimensional grid, each occupancy bit being equal to either a first value or a second value, each occupancy bit having a corresponding function value,
• setting each occupancy bit being equal to the first value if the corresponding function value is less than the isolevel, and to the second value if the corresponding function value is higher than the isolevel, and
• employing each occupancy bit value in said occupancy image embodied in a computer-readable material for use in at least one of a computer graphics application and a scientific visualization application to represent isosurface data.

An encoding apparatus comprising:

• means for determining values of occupancy bits of an occupancy image as a function of a 3D regular grid, a scalar function and an isolevel, and having mesh connectivity and a substantial first proportion of geometric information encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder, and having any remaining second proportion of geometric information in the form of one quantized scalar value per intersecting grid edge, and specifying the location the corresponding Marching Cubes vertex more precisely, being efficiently encoded in scan-order with the same mechanism, the means including:
• means for visiting nodes of the three-dimensional grid in scanning order,
• means for comparing a function value associated with each node with the isolevel,
• means for setting a value of the occupancy bit associated with each node to a first value if the function value is less than the isolevel, and
• means for setting the value of the occupancy bit associated with each node to a second value if the function value is higher than the isolevel.